' +JJJJ ?\>m0M='+l> /+l   d']6@5L&]655]6LF%5 & "L}"BB5L&]6 X  `6 7777777 7777JJJJx 77L? L7877777777 776i 7 7867 7`77 777777`x =(`(8`5775I7`B` 76`77`>J><;VU<)?<`8'x0|<&HhHh 8 8 8 8V&` aI꽌ɪVɭ&Y:&<&Y:&;: 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8 9: :' 9: :& :x)*++`FG8`0($ p,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?8  1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#000'#07#0:"4<*55**5*%5)1)1)1)'#0/#0*5*75**5*:5/#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!H(+ "@H !D)"E` @ $ C ` DQ &J80^݌Hh < <݌ < < h < < < <`HJ>݌h Hh݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 (G FG HZXj 80x D9$xxH` >( Z>h Z>L=.xxH >hh@(LH>9L>HH/Hh/ H?-З( 8(& 8$8 H` *8HNx`* >x$50x*$50xL9JJJJ`HHjf5 >h $50x`HA>VD;;P >(ED Z> ?$0x8x D9- 8DD# H8`?E Vˆʎ55L $ 5 55555 &a*5`*5` "L&5_*b*JL%u**Lz%`** $  Q(lXJ̥KlV $  Q(lV eօ3L e3L &%R*L &%Q*L d' "L4% N'e*)n*5 5 &`@-e*f*f* 5 "L# "5f*`L %.* *t*Q*L$ %L&*L` "O**P**u** d' "L% N'e*)n*o*o*n* &8ɍ` ^&f\*555L& ^&NR* & "R*ΩL&)\*Z* ʽ LH*v 3h`0h8` " ['L & N'С55 &5`*A*@` +5L^6L65`  \* ?*0 '\* '  Q( ^&\*lZl^?*c*q)H c*h`f*5h*5j*555@O*AP*`u*@`@5&`Q*R*`E 'Ls' ' ' @DAE@u*`8` %@ @A@`@`**@*A`M5 ) "L&`8@AW*c*@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@c*h8&ȑ@Hȑ@Ah@L'Hȑ@ȑ@* htphso`hMhL`9V*8U*897T*6S*67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- (   Ϡ734@~3!+,W,o,*--,,9,-.-~3~3,,,,~3~3,,,,~3_*3 j.5 *H*H`Lc3 (+L3 +55555 1^3_* )3J Q*L_3Ls3443 D23455545554 70 / 7 :/354545455454555535L^/5-5I5555 55` / 4/ 2-5! / 08555454 70L3 (+50+5B5C3 2 70L35 *H*H`Lg3L{3505 *H*H` 3 ,5L3 3 1 ,H 1hBL, 0 BH [1 1h`Lo3 35 ,L3 3 1B , 1L,H 0hB@ 55 [1L133 (+34) 34 70L3 3L3 (+ 055L- (+34L{33454445 70 ^/* / 3B0 HȱBh -355 -8 /L38 25` +5 /3 /. /. 3 E7D B. /. /. 0]34S0J4 4) 3 4D4E B. 4  /. 02L3 Ν3 3`HD٤33DEEhiHLG.h ` /5B5-` /5B-` + X05I33383 33DH /4 E03744Ȍ7 X040 7 J7L35B5C`,5p` / R0-55`50` K/ R0-55`575755` 4/ K/ /( 55L/BȱBL/58` D2BH5BH :/ 75Bȭ5Bhh55 R0B5m55ȱB5m55` /LR0557755`*7*75LR0 E0(33 48`433 R0` E033LR0*7*7`777 555I7575757577** 7757`7 L35555f /55555555 ^/`855 i /B58` 41L 15ȱB5 /5555 /5`3 D23ȑB55B5 / 7 55`5555555555 5555`555`55BC55`5555`L3 /5B5C355 0Q340"B4 3` 02۰Ϭ33B438`3i#`3ЗLw35!50>5555`53 /3m3 3 3733i35 3583 /35ЉLw35`H /5h 25L/~43 533`55555555J5m55m5jn5n5n5ۭ55m5555m55m55`"L? 585H ~.(3` # d ֠z# u*`arge square"::"(size 3 x 3).":9000~T9100:CO,20,120:"There are also some medium"::"size squares (size 2 x 2).":9000^GXX8:GYY8:US2:9800:9000:9600:9900hCL$:9600:Z$(1)"LARGE":Z$(2)"MEDIUM":Z$(3)"SMALL":CO:"So for the"::"3 9000S6N2:8800:CO:"We will keep track of"::"information on a chart.":9000@X110:Y50:GS3:CO,20,120:"Now consider a grid 3 units"::"on a side.":9600:C0:9000%J9100:CO,20,120:"There are now 9 small squares"::"(size 1 x 1) and 1 lgrid of just"::"2 units on each side. (2 x 2)":9600:C0:9000 "9100:CO,20,120:"There are 4 small squares"::"(size 1 x 1) and 1 large square"::"(size 2 x 2).":9000,9100:CO,20,120:"The total number of squares"::"is 5. (4 + 1 = 5)":C1:143:9200:9000 CO:"The simplest case of our"::"original problem of a 5 x 5"::"grid is a 1 x 1 grid.":AFT,4:CO,110,100:CN$"!"CO$ CO,20,140:"Clearly, it contains only 1"::"square.":9000@ X110:Y50:GS2:CO,20,120:"Now consider a 43:9200:9000 CO,10,50:"But simplifying the problem can":CO,50,85:"Be difficult if you can't":CO,50:"think of how to simplify.":CO,50,120:"Seem like a long, slow":CO,50:"way to get the solution." BL43:BR231:BU80:BD108:9200:BU115:BDWIND,WL,WT,WR,WB:9300 CO,10,50:"The simplifying method can":CO,50,85:"Help you get started on":CO,50:"a similar problem.":CO,50,120:"Help you see a pattern to":CO,50:"use to solve the problem." BL43:BR231:BU80:BD108:9200:BU115:BD1(10):3:QU$(34):SS$(1)"s":SS$(2)"is":SS$(3)"are":CC$(3):CO$:AFT,1Z xVSP:WIND I16:AN(I):I:1,5,14,30,55,91 ::START OF PROGRAM: 900,3:MAX100:C1:CO,0,10:CN$"SIMPLIFYING THE PROBLEM"CO$CC$:AFT,3:WL20:WR260:WT20:WB191:, PROGRAM [SQUARES-SIM]<DEVELOPER [LOIS EDWARDS][PROGRAMMER[RUSS ERICKSON]t(COPYRIGHT MECC 19832LAST MOD [6/13/83]d::INITIALIZE:i230,64:24576K n16384:CM$(13):D$CM$(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$    P pp(p  @@@h @ @ @ p pD @ @ p pDPPPPPPPP pp(p  @@@h @ @ @ p p pCN$:Z1US:CO,XX,YY(Z1)8:Z11US:"'";:::qW&T50:8700:Z1US:CO,XX,YY(Z1)8:Z11US:"#";:::\&8700:AFT,1:CO$:y"yWIND:HSP:VSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"Ĺ900,0:5000:RNH,"SQUARES-B"(((MAX)),N),Y$:OP((Y$)):OPMINOPMAXįCO,0,182:HSP,1:"Enter a number from "MIN" to "MAX" please.":HSP,2:9710%CO,0,182:CEL:WIND,WL,WT,WR,WB:H&M&UXUS1GSUYUS1GSUXUX1:UYUY1:98053R&AFT,4:XX(UX1)8GX:YY(UY1)8GY:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:=T$}^$WL(771):WRWL(772)(773)2561:WT(774):WB(775)1:%%AFT,4:CN$:Z1GS:GXX:GYY:CO,X,Y(Z1)8:Z11GS:"#";:::%AFT,1:CO$:%x%9300:WIND:CO,X,Y:INP,CL$:CO,0,90:"One moment please...":.!>"Z51T::D(#V2#CA$:SPACE:d<#C1ĺCL$jF#p##Z0:Z13:2:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZ7$ZZZ11:s sometimes"::"not the best method to use to"::"solve a problem.":CO,W,120:"Do you want to explore this"::"problem using a different"CO,W,154:"strategy? ";:36000:Z$"Y"480900,0:5000:RNH,"MENU"900,1:5000:RNH,"SQUARES-B"(90:"Do you want to try again? ";:36000:Z$"Y"ĬP9,yZ$"N"İ5000:RNH,"MENU"c9DB:GCP,ZX,ZY9CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no":360209CO,0,182:CEL: PPPPPPPnter a letter from A to "M$;CN$:99008&Z1((Y$,1)):Z2((Y$,1)):Z1Z2įCO,20,182:CEW:CO$"Please try again, "CN$Y$CO$" is a point."CN$:99008&Y$(Z1)(Z2):Z(Z1Z21Z1Z21)(Y$"AL"Y$"LA")8&CO,20,182:CEL:29yHSP:VSP:CL$CO$:CO,0,"Enter a number from 1 to "MAX:WIND,20,20:9700G7%CO,10,182:CEL:7H&CA$:CO,X,Y:INP,(1,LE$),Y$:Y$"A"Y$M$įCO,10,182:"Enter a letter from A to "M$:98007\&CO,10,182:CEL:%8&CO,X,Y:INP,(L,LE$,0),Y$:Y$"A"Y$MM$įCO,20,182:CEW:CO$"EZ,12)1:CO,SX(Z,I)9,SY(Z,I)2:(Z$,I1,1)::u6X%I051:228,H(H):SX(0,Z1)1,SY(0,Z1)SX(0,Z2)1,SY(0,Z2):I:6%P0N1:SIDE0P:X(P),Y(P)X(SIDE),Y(SIDE):SIDE:P:17%CO,X,Y:INP,(((MAX)),N),Y$:OP((Y$)):OP1OPMAXįWIND:CO,10,182:E1N:X(SIDE),Y(SIDE):SIDE:5:%SX(Z,0),SY(Z,0):X(0)SX(Z,0):Y(0)SY(Z,0):NSX(Z,12):SIDE1N1:SX(Z,SIDE),SY(Z,SIDE):X(SIDE)SX(Z,SIDE):Y(SIDE)SY(Z,SIDE):SIDE:SX(Z,0),SY(Z,0):5D%I0SX(Z,12)1:CO,SX(Z,I)2,SY(Z,I)4:"]":I:06N%I0SX(ZZ,BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZn4$ZZZ11:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:t4%4&%X(0)X:Y(0)Y:RAD3.14159262N:SIDE1N:XR(X((RADSIDE))L):YR(Y((RADSIDE))L):X(SIDE)X:Y(SIDE)Y:SIDE50%X(0),Y(0):SID0:BR276:9200:9000 3OP2:L3CL$:CO,0,90:"One moment please...":^3(#CA$:SPACE:k3<#CLĺCL$q3F#3#BOX,110,10,279,115:BOX,00,115,279,180::3#)4#Z0:Z13:2:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLe several strategies you"::"might use to solve the problem.":::"Three methods to try are:"CC$3AFT,1:WIND:CO,52,110:CN$"Trial and error":CO,12,130:"Making an exhaustive list":CO,20,150:"Simplifying the problem"CO$:WIND,W,W:BU103:BD170:BLZ1:9550:96001CO,120,20:VSP:"Here is a dodecagon"::CO,120:"with all of its"::CO,120:"diagonals.":CO,W,120:"The problem asks you to find"::"out how many diagonals there"::"are in all.":CL119000b2W10:WIND,W,W:VSP,1:"There ar,120:CN$"DJ"CO$" or "CN$"HL"CO$" are"::CO,120:"examples of other"::CO,120:"diagonals.":CO,20,120:"They each join 2 vertices that"::"are not next to each other."0Z0:Z15:Z211:9560:Z11:Z29:9560:9000:8981CL$:Z0:Z$LE$:9540:9530:R0Y$"AD"Y$"DG"Y$"FJ"Y$"DA"Y$"GD"Y$"JF")/FTR1:CO,120,20:"Not quite. Try"::CO,120:"again.":CO,20,120:"Name a diagonal different"::"from "CN$"AD"CO$", "CN$"DG"CO$" or "CN$"FJ"CO$".":9000:9400TR0:CO,120,20:"Oops!":::CO named"::CN$"GD"CO$" or "CN$"JF"CO$".":Z0:Z15:Z22:9560:Z13:Z211:9560:9000.9100:Y120:CO,20,Y:"Name a different diagonal."CN$:X233:9900:CO$:9100:Z0įCO,120,20:"That's correct."::CO,120:CN$Y$CO$" is a diagonal.":9000:8984/F(T0:AFT,2:::CN$"AD"CO$" is a diagonal of this"::"dodecagon. It could also be"::"named "CN$"DA"CO$".":Z0:H127:Z18:Z25:9560:9000:9100S.::CO,120:CN$"DG"CO$" and "CN$"FJ"CO$" are"::CO,120:"diagonals too.":CO,W,120:"They could also be:9000:1000t,CL$:Z$LE$:Z0:9540:9530:Z1:9550:CO,125,20:"In a geometric":CO,125,36:"figure, a diagonal",CO,125,52:"joins 2 vertices,":CO,125,68:"but it is not a":CO,125,85:"side of the figure.":BL117:BR279:BU12:BD106:9200-CL13:BR250:9200:HSP:9000g+AFT,3,6:CL$:CO:"Now you are ready to"::"try to solve the problem." ,:"Here is the problem statement:":CO,12,105:"What is the total number of":CO,12,115:"diagonals in a dodecagon?":BL5:BR243:BU96:BD132:9200L108:BR278:BU40:BD92:9200:HSP:VSP:WIND,W,W:CO,90,104:AFT,2:CN$"AE"CO$" and "CN$"CH"CO$" are diagonals."::HSP,1+AFT,3:HSP,1:CO,20,130:"A "CN$"Diagonal"CO$" joins 2 vertices that"::CO,20:"are not next to each other.":BU125:BD160:BLt to"::CO,120:"each other.":9000:898)AFT,3,0:VSP,4:WIND,115,0,279,191:9100:HSP,1:CO,115,8:"Not quite. It's easy to":"get confused, isn't it?"::AFT,3{*CO,115,48:"A "CN$"SIDE"CO$" joins 2 vertices":"that are next to each":"other.":B16368,0:32000R 230,64:D$"BRUN LOGO":16304,0:16297,0:16299,0:16302,0k $D$"BRUN Y2UTIL.OBJ" )RNH,"MUSIC.OBJ" .RFL,"PPRINT.OBJ" L975,255 1023,0 RNH,"MENU": }:BS(P(P(999))1)16:BS1BS7BS6 }:BS(P(P(%  P.S.SHELLO1COPYRIGHT(C)MECC1983F( L.M.8/10/84PWHLX32000D$(13)(4):P(X)(X)(X1)256(65435)6ĺD$"PR#0":D$"IN#0":16372,0 ::(978)157Ģ12:"THIS PRODUCT NEEDS AT LEAST 48K TO RUN.":16384,128:PPPPPPPP pp(p  @@@h @ @ @ p p@ p pp @ @ @ p pDtry again? ";:36000:Z$"Y"ĺD$"RUN DIAGONALS-B"O,yZ$"N"İ5000:RNH,"MENU"V iDB:GCP,ZX,ZYCO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020CO,0,182:CEL: 1:ZZZY9640,%X(P),Y(P)X(S),Y(S):S:2%8%%CO,X,Y:INP,(((MAX)),"-09"),Y$:OP((Y$)):OPMINOPMAXįCO,8,182:"Enter a number from "MIN" to "MAX" please.":9710%CO,10,182:CEL:y 1"yVSP:CL$CO$:CO,0,90:"Do you want to CO,SX(Z,I)2,SY(Z,I)4:"]":I:^N%I0SX(Z,12)1:CO,SX(Z,I)9,SY(Z,I)2:(Z$,I1,1)::X%I011:228,H(H):SX(0,Z1),SY(0,Z1)SX(0,Z2),SY(0,Z2):I:%%ZZ0:P0:S210:ZZZZ1:ZZZY9640%X(P),Y(P)X(S),Y(S)::P19:SP211:ZZZZ"not next to each"::CO,120:"other.":CO,20,160:"Which one is correct? ":X189:Y160:MAX2:9700(v9100:CO,0,0:CEL:WIND,W,W:OP1895))zCO,120,30:"Good work!":::CO,120:"A diagonal joins"::CO,120:"2 vertices that"::CO,120:"are not nex2)(Z1)CO$".":9000:9100'pWIND:CO,0,0:"Here are two descriptions:":CO,120,20:"1. A diagonal joins"::CO,120:"2 vertices that are"::CO,120:"next to each other."c(uCO,120,80:"2. A diagonal joins"::CO,120:"2 vertices that are"::CO,120:)CN$"CD JI HC":X90:Y141:L2:9900:CO$:Z895&fCL0:9100:CO,120,20:"You're remembering"::CO,120:"your geometric ideas"::CO,120:"well!"'k::CO,120:CN$Y$CO$" is a diagonal."::CO,120:"It could also be"::CO,120:"called "CN$(Zuickly review the"CC$::"idea of a diagonal."CC$:9000:900%R9100:CO,120,20:"Good! "CN$Y$CO$" is a"::CO,120:"diagonal. It could"::CO,120:"also be named "CN$(Z2)(Z1)CO$"."7&\CO,W,120:"Which of these names another"::"diagonal? "::10a diagonal"$>:"of this dodecagon? "CN$::10)"AB AE HG":H255:Z0:Z14:Z28:9560:Z17:Z28:9560:Z11:Z22:9560<%HM$"L":X150:Y140:Z2:9900:CO$:Z1İ9100:CO,120,20:"No, "CN$Y$CO$" isn't"::CO,120:"a diagonal.":CO,W,120:"Let's q*CO,30:"diagonals in a dodecagon?":BL20:BR260:BU70:BD115:9200:CO,35,140:"Do you know what a diagonal"::CO,35:"is? ";:36000:Z$"N"900 $4W5:WIND,W,10,279:CL$:Z$LE$:Z0:9540:9540:9530:Z1:9550:CO,W,120:AFT,2:"Which of these names ::CO,120:"Another side could"::CO,120:"be "CN$"BC"CO$" or "CN$"JK"CO$" or "CN$"LK"CO$".":Z0:Z16:Z27:9560:Z110:Z211:9560:Z19:Z210:9560:9000" CL$"Now think of the"CC$::"problem again."CC$::CO,30,78:"What is the total number of":#O$" isn't a side."::CO,130:"Try again.":::CO,120!"Remember... A side"::CO,120:"joins 2 vertices":AFT,3::CO,120:"that are "CN$"next to"::CO,120:"each other."CO$:AFT,2:9000:9100:740" TR0:9100:CO,120,20:CN$Y$CO$" isn't a side."Z0:Z11:Z22:9560:9000:9100 :CO,20,120:"Now you name another side."CN$:X230:Y119:L2:9900:9100:Z1ĺ:CO,120,50:AFT,3:"That's correct.":AFT,2::CO,150:Y$::CO,120:CO$" names a side.":9000:800 TR7806!TR1:CO,120,20:CN$Y$CAL"Y$"LA")"6&CO,20,182:CEL:(6y6"yWIND:HSP:VSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"ĺD$"RUN DIAGONALS-B"6,yZ$"N"İ5000:RNH,"MENU"66DB:GCP,ZX,ZY97CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"D"::"ERROR"CO$" does not make it easier to"::"solve another similar problem.":9000:"Without clues to tell you how good"::"your guess is, it is difficult"::"to make your next guess any"::"better.":9000CL$:CN$"TRIAL AND ERROR"CO$" ie: ";CA$;:GCP,ZX,ZY:TI$:PA$""įCO,ZX:PA$m>12:" Direct inquiries to:"::" "CC$;:GCP,ZX,ZYH:WIND,ZX,ZY,279:CO:"MECC Distribution":"3490 Lexington Avenue North":"St. Paul, Minnesota 55112":"(612) 481-3527"R30000:CL$:WIN00ZYY1İ30000::CO,X1,Y1:CEWnMN$(L)::" ";:GCP,ZX,ZY:WIND,ZX,ZY,279,191:L11DP:DS$(L,L1);:L1:WIND:::L:30000 *CL$:CO:VSP,10::"A manual to aid in the use of this diskette is available from MECC.":VSP/49:" Titlnt to try again? ";:36000:Z$"Y"įRNH,"DIAGONALS-B"S ,yZ$"N"İ5000:RNH,"MENU"[ n DB:GCP,ZX,ZY CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020 CO,0,182:CEL:AAhe num$):Z65Z65MMįCO,20,182:CO$"Enter a letter from A to "(64MM)" please."CN$:9910&Z1((Y$,1)):Z2((Y$,1)):Y$(Z1)(Z2):Z(Z1Z21Z1Z21)(Y$"AL"Y$"LA"Z1Z2)&CO,20,182:CEL:y 5 "yWIND:HSP:VSP:CL$CO$:CO,0,90:"Do you waZ$Y$:9570:9810p&ER1:9100:CO,145,25:CN$Y$CO$" is a diagonal, but it has already been drawn. Be careful! Do not list a diagonal twice. Keep listing!":9810& &CN$:CO,X,Y:L):CO,X,Y:INP,(L,LE$,0),Y$:CO$:(Y$)0Z1:9920V&Z(Y215:Y150:9900:Z0ıW&(FL1(Z165Z265))Z1İ9120:CO,145,25:ER1:CO$"Oops! Your":"finger must have":"slipped. "CN$Y$CO$:"can't be a":"diagonal"Z$(FL):"Try again.":9810\&Z3DO(Z1):Z4DO(Z2):Z4Z3Z5Z4:Z4Z3:Z3Z5f&MA%(Z3,Z4)10:ZZZZ1:ZZZY9640W%X(P),Y(P)X(S),Y(S):S:P19:SP211:ZZZZ1:ZZZY9640v%X(P),Y(P)X(S),Y(S):S:P|%% %Z1500::%CO,10,182:CEL:H& R&Z$(0)".":Z$(1)" from A.":AFT,2:WIND:L2:CO,145,150:"Diagonal:"CN$:X27:Z1DO(((Z$,1))):Z2DO(((Z$,1))):Z2Z1Z5Z1:Z1Z2:Z2Z5l%AFT,3,0:9560:MA%(Z1,Z2)0:CO,10,160:NDND1:CO$"Number of":CO,10,168:"diagonals: "CN$;ND;CO$:WIND,WL,WU,WR,WD:AFT,3,6v%ERER0:FL19400,9300%% %ZZ0:P0:S2Y(Z,S):X(S)SX(Z,S):Y(S)SY(Z,S):S:SX(Z,0),SY(Z,0):mD%I0SX(Z,12)1:CO,SX(Z,I)2,SY(Z,I)4:"]":I:N%I0SX(Z,12)1:CO,SX(Z,I)9,SY(Z,I)2:(Z$,I1,1)::X%I011:228,H(H):SX(0,Z1),SY(0,Z1)SX(0,Z2),SY(0,Z2):I:Ab%WIND:AFT,3:H1diagonals one at a time. Be organized! Work";$" from B, then C, etc."::"When you think they are "CN$"ALL"CO$" drawn, press an extra "CN$"RETURN"CO$".":AFT,3,6:% 7:%SX(Z,0),SY(Z,0):X(0)SX(Z,0):Y(0)SY(Z,0):NSX(Z,12):S1N1:SX(Z,S),SBDZZBLZ,BUZZ:ZZ1:ZZ_$ZZZB1:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:e%:%SX(Z,0),SY(Z,0):X(0)SX(Z,0):Y(0)SY(Z,0):NSX(Z,12):S1N1:SX(Z,S),SY(Z,S):X(S)SX(Z,S):Y(S)SY(Z,S):S:SX(Z,0),SY(Z,0):!D%I0SX(Z,12)1:CL$:CEW:CO,0,90:"One moment please...":5(#G2#CA$:SPACE:V<#CL1ĺCL$\F#b##BOX,110,15,279,115:BOX,10,115,260,180::##5:Z0:ZB3:ZZZB01:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,35:"Often we use "CN$"TRIAL AND ERROR"CO$::"methods to help us get started."BL0:BU20:BR260:BD73:9200:CO,8,120:"Then we move on and use a more"::CN$"SYSTEMATIC"CO$" method to solve the"::"problem.":90005000:D$"RUN DIAGONALS-EXH"/on.":CL1:9000W10:WIND,W,W:CO:CN$"TRIAL AND ERROR"CO$" isn't a very"::"systematic method of solving a"::"problem. Even if you happen to"::"find a solution, you may not know"::CN$"WHY"CO$" it is a solution.":9000OW8:WIND,W,W:CO,W,Y1:"'("CO$:CO,X,Y:INP,(2,"-09"),Z$:ZZ(Z$):75&5&CO,X,Y:L):CO,X,Y:INP,(L,A,0),Y$:Z(Y$):Z65ZMįCO,20,182:CO$"Enter a letter from A to "(M1)" please."CN$:9910 6&Z1((Y$,1)):Z2((Y$,1)):Y$(Z1)(Z2):Z(Z1Z21Z1Z21)(Y$"4%X(P),Y(P)X(S),Y(S):S:P#4%)4%4%CO,X,Y:INP,(((MAX)),N),Y$:OP((Y$)):OP0OPMAXįCO,10,182:"Enter a number from 1 to "MAX" please.":97104%CO,10,182:CEL:4&4 &ZZ1700:ZZ:4H&15R&AFT,2:CO,X8,Y1:CN$"&''":CO,X9,Z,I)4:"]":I:M3N%I0SX(Z,12)1:CO,SX(Z,I)9,SY(Z,I)2:(Z$,I1,1)::3X%I011:228,H(H):SX(Z,Z1),SY(Z,Z1)SX(Z,Z2),SY(Z,Z2):I:3%3%ZZ0:P0:S210:ZZZZ1:ZZZY96403%X(P),Y(P)X(S),Y(S):S:P19:SP211:ZZZZ1:ZZZY9640ZZ1:ZZN2$ZZZ11:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:T2%2:%SX(Z,0),SY(Z,0):X(0)SX(Z,0):Y(0)SY(Z,0):NSX(Z,12):S1N1:SX(Z,S),SY(Z,S):X(S)SX(Z,S):Y(S)SY(Z,S):S:SX(Z,0),SY(Z,0):3D%I0SX(Z,12)1:CO,SX(Z,I)2,SY(1#CO,100,100:"Add "F(K1)" + "K1" = "F(K)::CO,100:"to get the number"::CO,100:"for the "F$(K)".":CL1:9000:ZK:9180:1# 2#Z0:Z13:6:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ:,50:Z" is added.":9000:BOX,100,30,279,19120#b0#9120:ZZZ19:CO,31,56ZZ12:F$(ZZ)::0#CL$:CO,20,20:"Number of diagonals":20,28150,28:ZK1:9140:ZK1:9150:CO,37,35K12:AFT,2:CN$"&'("CO$:CO,100,40:Z1$(K5)::CO,100:Z2$(K5)41,34ZZ12:2((F(ZZ))));F(ZZ)::CO$:/#AFT,2:CN$:ZZ2Z:CO,58,13ZZ12:"%":CO,64,14ZZ12:CO$" +"ZZ;CN$::CO$:,0#AFT,2:X72:Y1312Z:CO,58,Y:CN$"%"CO$:9800:BOX,58,Y2,99,Y9:BOX,100,30,279,191:CO,64,Y1:" +"Z:ZZZZ5įCO,100BOX,0,115,279,180::.#31,52212,52:31,53212,53:132,36132,175:132,37132,175:AFT,3:CO,57,44:CN$"FIGURE":CO,139,36:"NUMBER OF":CO,139,44:"DIAGONALS"CO$.#ZZ0Z:Y56ZZ12:CO,31,Y:F$(ZZ):CO,167,Y:F(ZZ)::+/#AFT,3:CN$:ZZ0Z:CO,"::"strategy to solve a problem"::"- perhaps one that you thought of"::"yourself.":::CN$"THAT'S GREAT!"CO$CC$:9000-p31000-CL$:CO,0,90:"One moment please...":-(#-2#CA$:SPACE:-<#CL1ĺCL$-F#-#.#BOX,110,15,279,115:105:"Making an exhaustive list":CO,10,120:"Simplifying the problem"CO$,\BL0:BR260:BU84:BD140:9200:CO,20,150:"One of these could help you find"::CO,20:"the answer to your problem!":9000|-fWIND,W,W:CO:"Sometimes you will use a different54"::"diagonals."+RW0:WIND,W,W:::AFT,1:CN$"GOOD PROBLEM SOLVING!"CO$CC$:AFT,3:9000:"Whenever you're faced with a"::"problem you "CN$"DON'T"CO$" know how to do,"::"remember to try..."I,WWIND:CO,50,90:AFT,1:CN$"Trial and error":CO,5,,166,164:" ":I010:CO,166,164:CN$" "CO$:J0100:J:CO,166,164:CN$"54"CO$:J050:J:I:CL1:9000+HAFT,3:WIND,20,20:CL$:"By "CN$"SIMPLIFYING"CO$" the problem and"::"looking for a "CN$"PATTERN"CO$", you've"::"found that a dodecagon has nals one":"at a time. Start with the octagon and":"end with the dodecagon.":HSP,2:Z4:9180:K59:X167:Y56K12:9800:ZZF(K)İ9190:830)4BOX,155,Y2,190,Y8:CO,166,Y:F(K)k*>K:AFT,1:BOX,0,0,279,25:CO,70,5:CN$"THAT'S IT!"CO$:AFT,3:CO1:9000( HSP,2:WIND,20,20:CL$::"Now complete the chart"::"up through the dodecagon.":::"You should be able to predict"::"the number of diagonals by"::"continuing the pattern.":CL1:9000)*WIND:CO:HSP,1:"Fill in the numbers of diago:CO,100:"next number of"::CO,100:"diagonals after 9?":X42:Y82:9800:KZZ:BOX,34,80,70,90:Z4:9140:Z5:9150:9000:K14800(AFT,3:BOX,100,30,279,191:CO,100,40:"It's easy to"::CO,100:"add incorrectly!":::CO,100:CN$" 9 + 5 = 14"CO$:CLr.":::CO,100:"What number should"::CO,100:"be added to 9?":Z5:9160:ZZZ760&CO,100,50:"First 2 was added"::CO,100:"then 3"::CO,100:"then 4;"::CO,100:"now 5 should be added.":9000:BOX,100,30,279,191'CO,100,40:"What is the":hat is added"::CO,100:"to 0 to get 2?":Z2:9160}%CO,100,40:"Now what is added"::CO,100:"to 2 to get 5?":Z3:9160%CO,100,40:"Now what is added"::CO,100:"to 5 to get 9?":Z4:9160U&CO,100,40:"A pattern is"::CO,100:"becoming clea:":Z4:9120:CO,150,125:"As you predicted,":CO,150:"there are 14":CO,150:"diagonals in a":CO,150:"heptagon.":9000:800$WIND:CL$:"Let's look for a pattern together.":CO,20,20:"Number of diagonals":20,28150,28:Z3:91403%CO,100,40:"Wgonals.":9000#XBOX,34,80,65,90:BOX,80,30,270,90:Z4:9140:Z5:9150:CO,95,40:"You've figured out"::CO,95:"that there's an"::CO,95:"addition pattern in"::CO,95:"this sequence.":CL1:9000$bWIND:CO::"The chart would now look like this"D:CO,85,40:"What is the next"::CO,85:"number?":HSP,1:X42:Y82:9800:BOX,80,40,279,90:ZZ14įCO,85,40:"No, "ZZ" isn't the"::CO,85:"next number.":9000:700#NCO,85,40:"That's correct."::CO,85:"14 is the next"::CO,85:"number of diathe numbers"::CO,85:"of diagonals we've"::CO,85:"counted so far.":CO,34,81:CN$"&''("CO$!:CO,20,120:"Look for a pattern in this"::"sequence. Try to predict the"::"next number of diagonals.":CL0:9000:BOX,64,29,279,90:BOX,0,120,279,191number of"::"diagonals for figures like a"::"dodecagon without having to draw"::"and count all the diagonals.":9000 &CO:"Number of diagonals":20,28150,28:AFT,3:CN$:Z3:9140:CO,64,36:VSP,0,2:AFT,2:BR$:VSP,1,2_!0CO,85,40:"These are ethod, we'll stop"::"drawing simpler figures and see":"if there's a "CN$"PATTERN"CO$" in the"::"number of diagonals we've already"::"drawn and counted.":9000z W10:WIND,W,W::"If we find a "CN$"PATTERN"CO$", then"::"we can predict the CL$:"Add this result to the chart.":9120:9000AFT,3,0:W10:WIND,W,W:CO:"Now the simpler figures aren't"::"so simple any more! A seven-"::"sided figure is quite complicated.":9"At this point in "CN$"SIMPLIFYING"::"THE PROBLEM"CO$" m,0,22:CN$"BF"SS$"CE"SS$"CF"CO$", and "CN$"DF"CO$".":CO,140,80:"There are 9"::CO,140:"diagonals.":9000:510TR1:BOX,0,0,279,33:BOX,125,33,279,191:CO::"Good try. Count again. Be careful":CO,0,20:"not to count a diagonal twice.":48015:9560:Z13:9560}:CO,130,120:"A hexagon has"::CO,130:" diagonals.":125,152145,152:X132:Y142:9700:OP9510AFT,2:BOX,0,0,279,33:BOX,125,33,279,191:COqTR1ĺCJ$"The diagonals are "CN$"AC"SS$"AD"SS$"AE"SS$"BD"SS$"BE"CO$",":CO"A "CN$"HEXAGON"CO$" has 6 sides.":AFT,3,6:Z3:9540:9530:Z6:Z$"EDCBAF":9550WIND,130,20,279,191:CO,130,70:"Count the diagonals"::"as they are drawn.":CL0:9000:CL1WIND:Z3:Z10:Z224:9560::Z11:Z235:9560::Z12:Z24:9560:Z2ЯCO,130:"diagonals.":9000:460oTR1:CO,20,20:"Good try, but not quite.":CO,130,80:"Count again.":430WIND:CL$:"Let's add this result to the chart.":WIND,20,20:Z2:9120:9000QAFT,3,0:WIND:CO::"Let's look at one more figure."::,152145,152:MAX9:9700:OP5460[AFT,2:BOX,0,0,279,35:BOX,125,35,279,191:WIND:CO TR1TR0:CO:HSP,1:"It's easy to miscount! The diagonals":HSP,2::"are "CN$"AC"SS$"AD"SS$"BD"SS$"BE"CO$", and "CN$"CE"CO$".":CO,130,90:"There are 5"::TR0:CO,130,60:"Count the number"::CO,130:"of diagonals as"::CO,130:"they are drawn.":CL0:9000:CL1:Z2:Z10:Z22:9560:Z23:9560:Z11:9560:Z24:9560:Z12:9560":CO,130,120:"A pentagon has"::CO,130:" diagonals.":X132:Y142:125"are the only"::CO,135:"diagonals.":AFT,3,0:CO,0,160:"A "CN$"QUADRILATERAL"CO$" has 2 diagonals.":9000CL$;:"Let's add this to the chart.":Z1:9120:9000AFT,2,6:CO,20,20:"A pentagon has 5 sides.":Z2:9540:9530:Z5:Z$"DCBAE":9550:9560:Z11:Z23:9560::CO,135:"are diagonals."|CO,135,110:"A quadrilateral"::CO,135:"has diagonals.":162,142182,142:MAX9:X169:Y132:9700mBOX,0,0,279,60:OP2įBOX,130,65,270,160:CO,135,70:CN$"AC"CO$" and "CN$"BD"CO$::CO,135: ^$AFT,3,0:9110::CO:"Enter the remaining diagonals from A. Use A and another letter to name each diagonal."::"When you think they are all named, press an extra "CN$"RETURN"CO$".":AFT,3,6:$ /$AFT,3,0:9110:CO::"Enter the remaining PPPPPPPP pp(p  @@@h @ @ @SX(Z,0CĹ900,0:5000:RNH,"SQUARES-B"<3,yZ$"N"İ5000:RNH,"MENU"B3a3DB:GCP,ZX,ZY:9300:WIND3CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":360203CO,0,182:CEL:WIND,WL,WT,WR,WB:9920+2&(CH77CH10)UYMSUYUY1:9920S2&CH32G(UX,UY)1İ8500:8530:99202&CH32G(UX,UY)1:NSNS1:CO,218(NS10)7,57:NS:99202&CH13ı2'99202y3"yWIND:HSP:VSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"X1:UY1:CC16368:CI16384:CI,0:8520:9860:MS(GS1)US:NS01&Z$"'":9850:CC,0:CI,128:CH(CI)128((CI)224(CI)251)32:Z$"#":98501&(CH73CH11)UY1UYUY1:99201&(CH74CH8)UX1UXUX1:99202&(CH75CH21)UXMSUXUX1:0H&70M&UXUS1GSUYUS1GSUXUX1:UYUY1:9805o0R&AFT,4::Z$"#":9850:Z$"'":9850:8700:AFT,1::0z&XX(UX1)8GX:YY(UY1)8GY:CN$;:Z1US:CO,XX,YY(Z1)8:Z11US:Z$;::::CO$:0&I16:J16:G(I,J)0:::0&@1&AFT,4:U%AFT,1:CO$:/%>/%9300:DB:GCP,ZX,ZY:16368,0:WIND/%CO,ZX,ZY:INP,(((MAX)),N),Y$:OP((Y$)):OPMINOPMAXįCO,0,180:CEW:CO,0,182:HSP,1:"Enter a number from "MIN" to "MAX" please.":HSP,2:97200&WIND,WL,WT,WR,WB:CO,0,182:CEL:BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZj.$ZZZ11:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:p.T$.^$WL(771):WRWL(772)(773)2561:WT(774):WB(775)1:.%.%AFT,4:CN$:Z1GS:GXX:GYY:CO,X,Y(Z1)8:Z11GS:"#";:::/0003f<ff<cc>cc>>cc>0000000t` ```````fffffff~l6iɆpq{0`0``0`00000`Z<`~~6  SQUARES-B$DEVBYL.EDWARDS6BYR.ERICKSONG((C)MECC1983Z2LM84/08/20PWHtd230,64:24576:16384nD$(13)(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):QU$(34):SS$(1)"s":SS$(2)"is":SS$(3)"are":CC$(3)sAFT,1 x          W POOLINGAROUND0LOISEDWARDS&R.ERICKSON>(MECC1983N28/10/84PWHhd230,64:24576:16384nD$(13)(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):QU$(34):CC$(3)sAD34520274:233,(AD256):232,AD(AD256)256: xR(I)#BOX,145,10,279,180-#9040:CO$:CO:4# #6:Z0:ZB3:ZZZB01:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZ$ZZZB1:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:T$B:GCP,ZX,ZY{-:CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,W,182:"Type in yes or no."CC$:36020-CO,0,182:CEL: PPPPPPPP pp(p  @@@h @ @ @ p p8530:9920G,&CH32G(UX,UY)1:NSNS1:CO,217(NS10)8,57:NS:9920T,&CH13ı^,'9920d,y,"yWIND:HSP:VSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"Ĺ900,0:5000:RNH,"SQUARES-B",,yZ$"N"İ5000:RNH,"MENU", -DS(GS1)US:NS0I+&Z$"'":9850:CC,0:CI,128:CH(CI)128:Z$"#":9850o+&(CH73CH11)UY1UYUY1:9920+&(CH74CH8)UX1UXUX1:9920+&(CH75CH21)UXMSUXUX1:9920+&(CH77CH10)UYMSUYUY1:9920 ,&CH32G(UX,UY)1İ8500:X1:UYUY1:9805E*R&AFT,4:Z$"#":9850:Z$"'":9850:8700:AFT,1:*z&XX(UX1)8GX:YY(UY1)8GY:CN$;:Z1US:CO,XX,YY(Z1)8:Z11US:Z$;::::CO$:*&I16:J16:G(I,J)0:::*&+&AFT,4:UX1:UY1:CC16368:CI16384:CI,0:8520:M%DB:GCP,ZX,ZY:16368,0:9300:WIND)%CO,ZX,ZY:INP,(((MAX)),N,0),Y$:OP((Y$)):OPMINOPMAXįCO,0,182:HSP,1:"Enter a number from "MIN" to "MAX" please.":HSP,2:9720)&CO,0,182:CEL:WIND,WL,WT,WR,WB:)H&*M&UXUS1GSUYUS1GSUXU:ZZ1:ZZO($ZZZ11:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:V(T$ (^$WL(771):WR(772)(773)256WL1:WT(774):WB(775)1:(%(%AFT,4:CN$:Z1GS:GXX:GYY:CO,X,Y(Z1)8:Z11GS:"#";:::(%AFT,1:CO$:(% %))10:AN(ZZ):'"&'(#CA$:SPACE:6'<#C1ĺCL$:L'F#CO,41,182:CEL:S'# k'#BOX,0,80,279,191:'#BOX,0,0,185,191:'# (#Z0:Z13:5:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ0&!&"Z51T::&`" E&j"CL$:20,80260,80:140,60140,170&t"CO,58,60:"Size":CO,180,60:"Number":CO,50,70:"Square":CO,164,70:"of squares"&~"ZZ1N:CO,58,80ZZ10:ZZ" x ";ZZ:'"Q0āZZPPQ1:CO,1887(AN(ZZ)10),80ZZ10(N6hed press RETURN.":%\!%%a!QUS1n%f!N5:P1:8800:CO,W,20:"Now fill in that number on the"::"chart."&p!X188(MSMS10)7:Y90Q10:CO,X,Y:9700:BOX,W,20,279,50:OPMSMSįCO,W,20:"No, the correct answer is "MSMS".":CO,X,Y:MSMS" ":900x$M!CO,195,10:"Number of":CO,209,20:US" x "US:CO,202,30:"squares":BL208:BR238:BU50:BD70:9200:CO,218,57:" "%R!9100:CO,W,120:"To count the "US" x "US" squares,"::"move the cursor to a square and"::"press SPACE. When you are"::"finisS-B"0#CL$:CO,0,92:"One moment please...":6#4!#>!9100:CO,W,120:"Look again. You have already"::"counted that square.":9000:#H!CO,10,10:"To move cursor":CO,40,20:AFT,4:CN$;","CJ$;CH$"("CJ$CH$CH$CH$"%) *$"CJ$CH$CH$CH$"+"CJ$CH$"-"CO$ that's not it. The answer"::"is 385 squares in a 10 x 10 grid."::"Recheck your arithmetic and see if"::"you need to alter the method you"::"used.""::"Hope you enjoyed the challenge"::"of this problem.":9000#900,1:5000:RNH,"SQUARECONGRATULATIONS!"CO$" Your method":HSP,2:CO,W,30:"works!":CO,W,60:"That required some"CC$::"very good problem"CC$!:"solving skills!"CC$:BL63:BR216:BU55:BD110:9200:CO,20,140:"Hope you enjoyed the challenge.":9000:680"CL$:CO:"No,"worksheet to help you."CC$:9000s CO:"Try your method on a 10 x 10":CO,W,30:"grid.":X100:Y95:GS10:9600 CO,W,50:"How many squares are there in a":CO,W,60:"10 x 10 grid? ";:MAX999:9700:OP385670x!CL$:AFT,3:CO,W,20:HSP,1:CN$"::CO,150:CN$"AB"CO$"."::CO,120:"It could also"::CO,120:"be called "CN$"BA"CO$".":H255:Z0:Z17:Z28:9560:9000:9100 CO,120,50:"This is side"::CO,150:CN$"GH"CO$".":::CO,120:"It could also"::CO,120:"be called "CN$"HG"CO$"."::CL1:9000:8009100:CO,127,20:"A side of a":CO,127,36:"geometric figure":CO,127,52:"is named using 2":CO,127,68:"vertices that are":CO,127,85:"next to each other."BL120:BU12:BR274:BD105:9200:9000:9100:CO,120,50:"This is side"CO,120,20:"Good. "CN$Y$CO$" is a side."::CO,120:"It could also be"::CO,120:"named "CN$(Z2)(Z1)CO$"."CO,90,120:AFT,3,0:"A side joins 2 vertices"::CO,90:"that are next to each"::CO,90:"other.":AFT,3,6:BL83:BU115:BR279:BD170:9200120,20:"Good! "CN$Y$CO$" is a side."::CO,120:"It could also be"::CO,120:"called side "CN$(Z2)(Z1)CO$"."CO,W,120:"Which of these names another"::"side? "::CO,50:CN$"BF DJ HG KA"X60:Y140:9900:CO$:Z645n9100: EG GK";X153:Y135:L2:M$"L":9900:CO$:Z6509100:CO,120,20:"Oops! "CN$Y$CO$" is not a"::CO,120:"side.":CO,30,120:"Let's quickly review how to"::CO,30:"name a side of a geometric"::CO,30:"figure.":9000:700q9100:CO, PROGTEACHEROPTIONS.DES.LOISEDWARDSJPROGRAMMERRUSSERICKSON[((C)MECC1983n2 84/09/26NAMtdn230,64:24576:16384:X%(50),Y%(50),X1%(50),Y1%(50),C%(50),A%(50),CO%(12),M$(50),SC%(10),AD%(11),L%(11) xAD34590:XP150:YP90:XD1           :9200:9000lAFT,3:CO:"Now that you see the pattern, try"::"to think of a way to find the"::"answer without having to count"::"squares "CN$"OR"CO$" make a new chart.":9000" vCO,W,60:"You may want to use"CC$::"a calculator and the"CC$::s a lot of work.":9000X"You have applied what you"::"learned about the 5 x 5 grid"::"to a new situation -- the 6 x 6"::"grid." bCO,W,120:" The pattern helped you generalize":CO,W,130:"to solve a new problem."CC$:BL3:BR274:BU115:BD145find the total number of"::"squares in a 6 x 6 grid."{D170,150200,150:CO,178,140:"+":CO,142,155:"Total 91":9000NCL$:CO:"So a 6 x 6 grid would contain"::"91 squares. That's a lot of"::"squares to have to count!"::"The chart saved ut as we did"::"before.":9000n&N6:P1:Q5:8800:CO,W,20:"Fill in the missing number.":CO,188,90:97000OP36įBOX,20,20,279,40:CO,W,20:CEL:"No, the correct number is 36.":CO,188,90:"36 ":C0:9000:C17:BOX,W,20,279,40:CO,W,20:"Now "is that the number of squares of"::"a given size is a "CN$"PERFECT"::"SQUARE"CO$"."CO,W,100:"We can apply this pattern"::"to the case of a 6 x 6 grid.":9000X110:Y20:GS6:9600:CO,W,120:"Here is a 6 x 6 grid."::"We can make a charer perfect"CM$CJ$"square after 25?"CM$CJ$" = 6 X 6":CO,X,Y:9700OP36ĺCL$:CO,W,20:"No, the next higher perfect"CM$CJ$"square after 25 is 36."CM$CJ$" (6 x 6 = 36)":9000YW5:WIND,W,20:VSP:CL$:"The "CN$"PATTERN"CO$" we have found"::*BL12:BR252:BU20:BD170:9200:9000X20:Y56:CO:"A "CN$"PERFECT SQUARE"CO$" is the"::"product of a number times"::"itself.":I511:CO,80(II10)8,150I10:II" = "I" x "I:I:9000EW10:WIND,W,W:CO,W,20:"What is the next highnumber would come above 25 to continue this pattern? ";:9700:OP36įCO,200,60:36:9000:520WIND,20,20:VSP:CL$:CO,20,40:"Each of these numbers"CC$::"25, 16, 9, 4, 1"CC$::"has a special property."CC$::"It is a "CN$"PERFECT SQUARE"CO$"."CC$e chart? ";:DB:GCP,ZX,ZY:CA$:WIND,W,20,188,191:I15:CO,200(AN(I)10)7,I1060:AN(I)::BL191:BR221:BU50:BD125:9200:CO,ZX4,ZY:36000:X79:Y154:WIND,20,20,140,190:VSP,8^Z$"Y"İ9120:CO:"Good, there is a pattern here."::"What W0:WIND,W,W:CO,W,100:"the information collected"CC$::"during exhaustive listing can"CC$::"provide an extra bonus."CC$BL20:BR256:BU95:BD150:9200:90003CO,W,20:"Can you see a pattern"::"in the numbers you":CO,W,54:"added on th"similar problems."CO,W,130:"A "CN$"PATTERN"CO$" helps"CC$::"us "CN$"GENERALIZE"CO$"."CC$:BL70:BR208:BU117:BD167:9200:9000CO:"Exhaustive listing can be tiring"::"but it usually works well if it"::"is done carefully,"::"and"CC$$:AFT,3:BL10:BR270:BU55:BD85:9200tCO,W,120:"Hope you aren't too"CC$::"exhausted to continue."CC$:9000CO:"Often the information collected"::"on a chart shows us a "CN$"PATTERN."CO$:::"We can use this "CN$"PATTERN"CO$" to solve"::"Total 55":C1:9000:AFT,3:CO,W:"From the "CN$"CHART"CO$" you know"CC$:"that the 5 x 5 grid contains"CC$::"a total of"CC$::"55 squares."CC$:9000'CO,W,20::"Exhaustive listing worked."CC$::::AFT,1:CN$"You solved the problem!"CO$CC? ";:9700:OP1İ9100:CO,W,120:"Look again. There is just 1"::"square of size 5 x 5.":9000|Q4:MS1:C0:8540:C1:BOX,W,20,279,50:CO,W,20:"Now add the numbers in the"::"right hand column.":170,140200,140:CO,178,130:"+"LCO,142,145:" squares.":9000T9900:NSMSMSİ9100:CO,W,120:"Look again. Actually there are"::MSMS" squares of size "US" X "US".":9000^8540:US:C1:CC,0hCL$:X120:Y20:9600:CO,W,120:"Finally, how many 5 x 5 squares"brCO,W,136:"are thereny 1 x 1"::"squares there are, type that"::"number. Otherwise press"FCO,W,172:"RETURN. ";:MAX100:9700:B1(OP25):W10:WIND,W,WJC0:USB4:B2MS5:Q0:B0:8550O9860:US1ĺCL$:X120:Y20:9600:CO,W,120:"Now count the "US" x "USelp you count the squares.":9000@W10:WIND,W,W:X120:Y20:GS5:9600:CO,W,120:"First we will count all the 1 x 1"::"squares, then fill in that"::"number on the chart.":C0:9000:9100:C1IEW0:WIND,W,W:CO,W,120:"If you already know how ma,64,105:"show":CO,100,120:"PATTERNS",BL93:BR167:9200:CO,173,120:AFT,4:CN$"&&$"CO$:AFT,3:CO,159,105:"lead to":CO,206,120:"SOLUTIONS"CO$:BL199:BR279:9200:9000!6WIND,20,20:N5:P0:Q0:8800:CO:"A chart like the one below can"::"hormation you collect"CC$::"about a problem."CC$:9000 WIND::"When you find a "CN$"PATTERN"CO$CC$::"you often can see how to"CC$::"solve the problem."CC$:CO,11,120:"CHARTS"'"BU114:BD132:BL5:BR61:9200:CO,67,120:AFT,4:CN$"&&$"CO$:COou speed up"::"the listing and counting process.": CO,W,100:"A "CN$"CHART"CO$" can help keep track"::"of the items we list, to avoid"::"confusion.":90007 :"Making a "CN$"CHART"CO$" often helps"CC$::"you see a pattern in the"CC$::"infCO,50,110:"Make you confused as to": CO,50:"whether you've counted":CO,50:"one possibility twice or":CO,50:"missed a possibility."CO$ BL43:BR245:BU75:BD93:9200:BU105:BD150:9200:90005 W5:WIND,W,W:CO::"The computer can help y.":CO,50,120:"Help you find all the":CO,50:"possibilities and count":CO,50:"them to find the answer."CO$ BL43:BR245:BU75:BD103:9200:BU115:BD150:9200:9000& CO,20,40:"But exhaustive listing can also":CO,50,80:CN$"Take a long time.":e":CC$(3):AFT,1! xVSP:WINDF I05:AN(I):I:36,25,16,9,4,1 1022,2:C1:CO,0,10:CN$"EXHAUSTIVE LISTING"CO$CC$:AFT,3:W10:WIND,W,Wn CO,20,40:"The exhaustive listing method can":CO,50,80:CN$"Help you understand the":CO,50:"problem% SQUARES-EXH(DEVBYLOISEDWARDS@PROGBYRUSSERICKSONW(COPYRIGHTMECC1983l2L.M.84/09/14PWHd230,64:24576 n16384:CM$(13):D$CM$(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):3:QU$(34):SS$(1)"s":SS$(2)"is":SS$(3)"ar                      "vertices are named using"CC$::"the letters A - L."CC$:CL0:9000:9100l:CO,120,20:"The vertex letters":CO,120,40:"help name the sides."vCO,30,115:"Which of these names a side of"::CO,30:"this dodecagon?":AFT,2::CO,50:CN$"AE CD        :Z$:Z$Z$"+"((ZZ1)(ZZ1)):ZZ;-"WIND,WL,WT,WR,WB:A-(#S-2#CA$:SPACE:a-<#C1ĺCL$g-F#m-#-#BOX,0,80,279,191::-#BOX,0,0,279,54:-#%.#Z0:Z13:5:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,rrect.":CO,20,120:"Do you want to try another":CO,20,140:"guess? ";:36000:BOX,0,90,279,191:Z$"Y"400AFT,3:CL$:"The "CN$"TRIAL AND ERROR "CO$"method does"::"not help you "CN$"generalize"CO$".":W:"Solving one problem by "CN$"TRIAL AN115:Y40:GS6:9600AFT,3:CO,W,100:"How many squares are there?":Y100:X230:9700:BOX,0,90,279,191:OP91įCO,20,120:CN$"That's right!"CO$CC$::"There are 91 squares."CC$:9000:420lCO,20,100:PL(OP1):"No, "OP" square"SS$(PL)" is not coilar"::"problem by using what you learned."rAFT,1:CO,W,100:"Using the same ideas to"CC$::"solve another problem "CC$::" is called "CC$::CN$"GENERALIZATION "CO$CC$|BU94:BD172:BR240:BL38:9200:9000CO:"Here is a 6 x 6 grid.":X"There are 55 squares in this grid."CC$:9000:360^CO,20,140:"Do you want to try another"::CO,20,160:"guess? ";:36000:Z$"Y"310c450-hCL$"Now that you have solved this"::"problem using trial and error,"::"see if you can solve a sim(OP1):Z(OP55)(OP55)2(OP55)3:Z320,330,340@CO,20,120:"There "SS$(PL2);CN$" MORE"CO$" than "OP" square"SS$(PL)".":350JCO,20,120:"There "SS$(PL2);CN$" FEWER"CO$" than "OP" square"SS$(PL)".":3503TCO,0,120:"You are right!"CC$::next guess"::"even better.":CO,W,140:"Do you want to try guessing the",CO,W,160:"number of squares? ";:36000:Z$"N"47056CL$:MAX100:X120:Y60:GS5:9600:Y120:CO,W,Y:"How many squares are there?":X226:9700:BOX,0,110,279,191:AFT,3:PL00 "The computer program has been"::"told how many squares there are."::"It will tell you whether your"::"guess is correct or not.":9000J""It will also tell you whether your"::"guess is too high or too low, so"::"that you can make your er.":9000 "In this problem it is easy to"::"guess a number of squares, but very"::"hard to check if your guess is"::"correct --- unless the computer"::"helps you." :"It's hard to know if you've"::"found "CN$"ALL"CO$" the squares.":90::CO,50,100:"Make you feel frustrated."CO$:AFT,1:BR252:BU65:BD83:9200:BU95:BD112:9200 AFT,3:9000:W0:WIND,W,W:9300::"To use trial and error method, you"::"need to have a way of knowing"::"when you have guessed the correct"::"answCO,50,130:"Solve some kinds of":CO,50:"problems."CO$:AFT,1 BL43:BR212:BU65:BD92:9200:BU95:BD122:9200:BU125:BD152:9200:9000` CO,20,30:AFT,3:"But, the trial and error method"::CO,20:"can also":CO,50,70:CN$"Take a lot of time."(3):AFT,1 xVSP:WIND! { C1:CO,0,10:CN$"TRIAL AND ERROR"CO$CC$:CO,20,40:"The trial and error method can":? CO,50,70:AFT,3:CN$"Help you get started":CO,50:"solving a problem.":CO,50,100:"Lead you to a better":CO,50:"method.":: PROGSQUARES-T&E,DEVBYLOISEDWARDSDPROGBYRUSSERICKSON[(COPYRIGHTMECC1983n2LM84/08/08PWHd230,64:24576 n16384:D$(13)(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):3:QU$(34):SS$(1)"s":SS$(2)"is":SS$(3)"are":CC$           1DXL,Y1DYLX1DXL,Y1L:1:L02:9,6L432L,6L:2352L,6L269,6L:9,183L392L,183L:2392L,183L269,183L:XbCL$TI$CC$:PA$""ĺPA$CC$lVE$CC$:::GCP,X1,Y1CO,X1,Y1:CEW L1NP:GCP,ZX,ZY:ZY10:RNH,"MENU" DB:GCP,ZX,ZYCO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020CO,0,182:CEL: PPPPPPPP pp(p  @@@h @ @ @ p pD X:YY(UY1)8GY:CN$:Z1US:CO,XX,YY(Z1)8:Z11US:"'";:::W&T50:8700:Z1US:CO,XX,YY(Z1)8:Z11US:"#";:::\&8700:AFT,1:CO$:yWIND:HSP:VSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"Ĭ ,yZ$"N"İ500:%AFT,1:CO$:%CO,X,Y:INP,(((MAX)),N),Y$:OP((Y$)):OPMINOPMAXįCO,10,182:HSP,1:"Enter a number from "MIN" to "MAX" please.":HSP,2:9700%CO,10,182:CEL:H&UXUS1GSUYUS1GSUXUX1:UYUY1:9805DR&AFT,4:XX(UX1)8G3:1:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZ$ZZZ11:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:%AFT,4:CN$:Z1GS:GXX:GYY:CO,X,Y(Z1)8:Z11GS:"#";:::BD166:9200:9000:CL$:275ICL$:CO,0,90:"One moment please...":hX5000:D$"RUN SQUARES-T&E"b5000:D$"RUN SQUARES-EXH"l5000:D$"RUN SQUARES-SIM"!Z51T::(#CA$:SPACE:<#C1ĺCL$F##BOX,0,100,279,191:w#Z0:Z1120:Y70:9600:W0:WIND,W,W:CO::"Now that we have noted some facts"::"about the squares, let's state the"::"problem again."CO,10,115:"The question is:":CO,10,136:CN$"How many squares are "CC$:"there in the grid?"CO$CC$:BL35:BR248:BU130,166:"5 Largest"PZ0:I24:X121:Y116(I10):9700:ZZ(OPI)::Z3500BOX,0,80,279,191:I24:CO,10,120:"There are squares with a side of"::I" units.":USI:II15:UXRA(6US)1:UYRA(6US)1:JI15:9800:JI:II:9000:ICL$:X10:WIND,W,W:CO,W,140:"Are there any squares with"::"sides between 1 and 5 units? ";:36000:Z$"N"4909100:CO,10,80:"What are the lengths of the sides"::"of these in-between squares?":CO,100,110:"Length":CO,121,126:"1 Smallest":CO,1219100:CO,W,120:"Look for the biggest square."::"What is the length of its"::"side? units"X50:Y156:9700:OP5İ9100:CO,W,140:"Look again. The side of the"::"largest square is 5 units.":US5:UX1:UY1:I110:9800::9000l9100:Wallest size square."::"What is the length of its"::"side? units"X50:Y166:9700:OP1įBOX,0,0,115,100:9100:CO,W,140:"Look again. The side of the"::"smallest square is 1 unit.":US1:UX1:UY1:I110:9800::9000cBOX,0,0,119,100:$"UNIT."QU$:CO,160,20:CN$"%&"CO$" Unit":CO,65,52:"Unit "CN$"&$"CO$:9000BOX,0,0,119,100:BOX,160,0,279,100:9100:W5:WIND,W,W:CO:"Here are more"::"questions to":H"help you "::"understand the"::"problem.":CO,5,130:"Look for the smunt?"QU$:9000X120:Y20:9600:CO,5,120:"Let's label the figure.":AFT,4:CO,180,35:CN$"%& "CO$"Grid":CO,5,135:"The whole figure is called a "QU$"GRID."QU$:C0:9000LCO,5,150:"The length of one segment of a side":CO,5,165:"is called a "QU36000:Z$"N"31020|WIND,0,10:9020:X200:Y20:9600:CO:"First ask yourself some"::"questions to find out"::"what you know about"::"this figure."CO,0,120:"Like "QU$"What do we mean by 'square'?"QU$::"or "QU$"Which squares should we co0,10,279:"Very good. Either you are an"::"excellent problem solver or you've"::"solved this problem before.":370h::"That seems like a wild guess."rCO,10,120:"Do you want to see some methods"::CO,10,140:"for solving this problem? ";:(OP25OP55)2(OP55)3(OP55)4:Z330,340,350,360J"Good, but there "SS$(PL2)" even more"::"than "OP" square"SS$(PL)" in this grid.":370T"Good, you've found more squares"::"than most people see on their"::"first try.":370w^WIND,1269,6269,33:267,159267,185:269,158269,185a 6:X10:Y10:X2278:Y2191:DX18:DY12:L02X1DXL,Y1LX2DXL,Y1LX2DXL,Y1DYLX2L,Y1DYLX2L,Y2DYLX2DXL,Y2DYLX2DXL,Y2LX1DXL,Y2LX1DXL,Y2DYLX1L,Y2DYLX1L,Y1DYLXe.":9000hAFT,2,0:Z0:9120:9000:WIND:CO::"Now let's look at a "CN$"QUADRILATERAL"CO$"."::"That's a 4-sided figure.":AFT,2,6:WIND,20,20:Z1:9540:9530:Z$"DCBA":Z4:95502rH127:CO,135,70:AFT,2:CN$"AC"CO$" and "CN$"BD"CO$:Z1:Z10:Z22 triangle. There are "CN$"NO"CO$::"diagonals in a triangle.":9000 ^W15:WIND,W,W:CL$"A "CN$"TRIANGLE"CO$" has 0 diagonals.":::"Let's enter that in a chart to"::"help keep track of the number"::"of diagonals in the simpler"::"figures we usCO,130,120:"A triangle has"::" diagonals.":130,152150,152:X137:Y142:MAX9:9700:AFT,3,0:OP0350ETW10:WIND,W,W:CL$"Good try. However, there's no"::"way to join two vertices of a"::"triangle without getting a "CN$"SIDE"CO$::"of thegon.":CO,0,100:"Let's start with a "CN$"TRIANGLE"CO$"."CC$::"It has 3 sides."CC$:9000@AFT,3,6:Z0:9540:9530:WIND,130,20,279,190:CO:"Remember... a"::"diagonal joins 2"::"vertices, but "CN$"CAN'T"CO$::"be a side of the"::"figure."mJ:WIND,W,W:CO,W,50:"If there is a "CN$"PATTERN"CO$", we can"::"predict the number of diagonals in"::"a dodecagon without having to draw"::"them all in and count them.":9000Z6CO,W,50:CN$"SIMPLER"CO$" figures have fewer sides"::"than a dodecau"Now that we've "CN$"SIMPLIFIED"CO$" the"::"wording of the problem, let's"::"count the number of diagonals"":"in some simpler figures.":::"Then we can see if there is a"::CN$"PATTERN"CO$" in the number of"::"diagonals.":9000,W05:BU43:BD72:9200gCO,20,87:"might be easier to understand"::"if it were simplified this way:"CO,34,130:"What is the total number":CO,34,140:"of diagonals in a "CN$"12-SIDED":CO,34,150:"FIGURE?"CO$:BL25:BR255:BU122:BD162:9200:9000 examples":" of the problem and then":" find a pattern which":" leads to a solution.":BU118:BD163:9200:9000"For example, the problem:":CO,34,50:"What is the total number of":CO,34,60:"diagonals in a "CN$"DODECAGON?"CO$:BL25:BR25:BU141:BD161:9200:CL1:9000 "To simplify a problem, you can"::CO,20,70:AFT,3:" * Use simpler words or":" numbers to help you":" understand the problem":" better.":BL20:BR250:BU63:BD110:9200:9750{::" * Look at smaller0:WIND,W,W:AFT,1:HSP,2:CL$::"Let's tackle this diagonal"::"problem again, trying a method"::"which doesn't involve making a"::"long exhaustive listing." CO,20,120:"This method is called:":::CN$" SIMPLIFYING THE PROBLEM"CO$:BL20:BR266n",9,"Heptagon",14,"Octagon",20,"Nonagon",27,"Decagon",35,"Undecagon",44,"Dodecagon",54 I04:Z1$(I),Z2$(I):: "You must have","added incorrectly.","Oops! You","misadded.","It's easy to","add incorrectly.","Not quite!","","Almost!","" W2137,94,94,62,49,10,66,6,20,120,63,145,106,120,106,70,63,45,20,70 4,17,137,123,148,125,72,30,88,5,9,120,70,144,110,100,70,40,9,58,6,19,117,70,152,120,117,120,67,70,37,19,67W I09:F$(I),F(I):: "Triangle",0,"Quadrilateral",2,"Pentagon",5,"HexagosAFT,1:HSP,2:CO$ xH(I)((228)I)0((228)0)I:BR$CN$"!"CJ$CH$(34)CJ$CH$"#"CJ$CH$"$"CO$:M12:VSP:WIND S06:SX(S,12):I0SX(S,12)1:SX(S,I),SY(S,I)::@ 3,28,92,112,144,56,48,4,21,132,112,136,112,80,35,92,5,10,120,62,/ DIAGONALS-SIM(DEVBYL.EDWARDS:BYR.ERICKSONK((C)MECC1983^2LM84/08/09PWHddwi230,64:24576n16384:SX(6,12),SY(6,12),X(20),Y(20):D$(13)(4):CL$(12):CN$(14):CO$(15):3:CC$(3):CJ$(10):CH$(8):SS$CO$", "CN$                :"that you might wish there"::"were another method to try.":9000e5000:D$"RUN DIAGONALS-SIM"CL$:CEW:CO,0,90:"One moment please...":(# 2#WIND::SPACE<#CL1ĺCL$P#WIND,WL,WU,WR,WD:CO:# #BOX,145,10,279,191:9130ANY PARTS":"TWICE"CO$&9000:9040WR265:9040:CO,WL,50:CN$"EXHAUSTIVE LISTING"CO$" works best"::"to solve problems in which the"::"list isn't too long.":9000DCO,WL,50:"This diagonal problem had a"::"long enough list of diagonals":too exhausted to go on!":CL1:9000c:"When you make an exhaustive"::"listing...":::AFT,3WIND,32:CO,32:"*"::"*":::"*"CN$:WIND,47,WU:CO,47,74:"WORK SYSTEMATICALLY"CO$::CN$"DON'T LEAVE OUT ANY":"PARTS"CO$:9700::CN$"DON'T NAME D:Z$"Y"İ9400:370AFT,3,0:VSP:CL$:WL20:WU20:WB170:WR250:9040:CO,20,37:"There are 54 diagonals"CC$::"in a dodecagon."CC$:BL39:BR230:BU30:BD70:9200#CO,20,120:"Hopefully, after doing this"::"exhaustive listing, you're not"::"8:9000:9100hAFT,3:94008rFL0:9800:ND54400|9020:BOX::"You're getting close! There are still some diagonals that you haven't listed."::"Do you want to go back and fill in the missing diagonals? ";:WIND:36000:WIND,WL,WU,WR,W800:ND9ER1:9120::"Check the drawing":"Not all the diagonals from A are listed yet.":"Keep listing!":340 ^9120:9100:CO$"Good work!":"You've listed all the diagonals from A."::"Now let's go on to the diagonals from B, C, and so on.":WUWUach vertex before moving to the next vertex.":9000:91006AFT,2::::"Let's start with vertex A."::"The first two diagonals are "CN$"AC"CO$" and "CN$"AD"CO$"."@MA%(1,1)1:MA%(1,2)1:Z$"AC":9570:Z$"AD":9570:9000:9100J9300qTFL1:9here are, you will ";""have to name "CN$"ALL"CO$" the diagonals."::"Then the computer will draw them in and count them for you.":CL0:9000:9100:BOX,0,0,279,99,:"Hint..."::CN$"BE SYSTEMATIC!"CO$:::"List "CN$"ALL"CO$" the diagonals from ehis works in the"::"dodecagon problem.":9000AFT,1,6:WIND:CO:"Here is the dodecagon again.":Z0:9540:9530:Z1:Z$LE$:9550:WL145:WU10:WR279:WD180:WIND,WL,WU,WR,WDCO:VSP,3:"To use exhaustive listing to find out how many diagonals tes in your listing."::"That is, you use up or write down"::CN$"ALL"CO$" the parts of the problem.":9000/"The solution to the problem may"::"then be the listing itself or"::"the total number of possibilities"::"listed.":::"Let's see how tCO$" the": "possible parts of the problem in"::CN$"AN ORDERLY MANNER"CO$".":BL0:BU72:BR270:BD130:9200:WL10:WR270:9000 CO,WL,50:"It is called an "CN$"EXHAUSTIVE"::"LISTING"CO$" because you exhaust "CN$"ALL"CO$:l "the possibilitiem.":CO,10,100:"It's called" ::CN$;7);"Making an":" Exhaustive Listing"CO$:BL25:BR230:BU120:BD160:9200:CL1:WL10:9000:AFT,3 "To solve a problem by making an"::"exhaustive listing, you":CO,10,80:"Write down or draw in "CN$"ALL",122,100,122,70,107,44,81,29,51,29,25,44,10,70,12,10,100,27,130,57,148,92,148,122,131,140,101,140,66,123,36,93,18,58,18,28,35,10,65  WU20:WL10:WD170:WR260:WIND,WL,WU:CO,10,40:"Let's look at another method of"::"solving this diagonal probl1:CO$` xH(I)((228)I)0((228)0)I:DO(I)73I(I73)12:LE$"IHGFEDCBALKJ":MM12:VSP S01:SX(S,12):I0SX(S,12)1:SX(S,I),SY(S,I):I:S:S210:MA%(0,S)1::P19:SP211:MA%(P,S)1:: 12,10,100,25,126,51,141,81,141,107,126 PROGDIAGONALS-EXH/DES.BYLOISEDWARDSFPROG.BYR.ERICKSON](COPYRIGHTMECC1983q2L.M.8/20/84PWHwdi230,64:24576n16384:SX(1,12),SY(1,12),X(20),Y(20),MA%(9,11):D$(13)(4):CL$(12):CN$(14):CO$(15):CC$(3):3 sAFT,          !z#   ŮԠ ٲ̮ʠ  ҠӠ!ˮΠ Ϡîʠٲ̮ʠ ҠӠˮΠӮΠ ՠ ӭԦŠ ӭȠ'ӭ͠. Ǡׯˠ2 ǠĠ ԮʠɠĮԠ͠ǠǯϠ ӭ 4 ӭԦŠӭȠӭ͠1 ӭ 3:9900:NS4İ9100:CO,W,120:"Actually, there are 4 squares"::"of size 3 x 3. The computer will"::"outline them one by one.":8600:90009100:CO,20,120:"There is also one 4 x 4 square.":9000ICL$:X120:Y30:9600:CO:"So for the"::"9İ9100:CO,W,120:"Actually, there are 9 squares"::"of size 2 x 2. The computer will"::"outline them one by one.":8600:90009100:CO,W,120:"There are 9 squares size 2 x 2."::"Now count the 3 x 3 squares.":9000X120:Y30:GS4:9600:US 4 grid.":GS4:X120:Y30:9600:9000w9100:CO,20,120:"How many 1 x 1 squares are"::"there? ";:9700:OP16480WIND,W,20,279,191:9100:CO,W,120:"Look again. There are 4 times 4"::"small squares. Or 16 squares.":9000US2:9900:NS You have found a "CN$"PATTERN"CO$" already! Now guess the total number for a 5 x 5 grid."VSP:CO,177,128:"1+4+9+16":CO,20,140:"5x5":CO,100,140:9700:Z(OP55)(OP55)2:Z600,610%WIND,20,20,260,191:VSP:CL$:CO,20,120:"Here is the 4 xa 4 x 4 grid? ";:36000:VSP:Z$"N"4509120:CO,20,20:"Enter your guess.":CO,20,128:"4x4":CO,100,128:9700:9120:CO:VSP,4OP30ĺ"No, that's not quite it. Let's go on and count the squares in the 4x4 grid.":9000:450\AFT,3:"Good!he chart.":CO,20,116:"3x3":CO,185,116:Z$MAX100:MIN1:CO,100,116:9700:OP14İ9120:CO:"No, we found the answer to be 14.":CO,100,116:"14 ":9000(9120:WIND,10,20,270,191:VSP,4:CO:"Do you want to guess the total number of squares in I)" squares ("ZZ" x "ZZ")":CO,X,Y:9700:OPIIįCO,20,170:"No, the answer is "II"."CC$:CO,X,Y:II" ":9000:CO,20,170:CEL:wI:CO,20,180:CEL|30,150220,150:CO,32,153:"14 Total squares":9000,N2:8800:CO:"Now add this total to tium"::"size squares (size 2 x 2).":9000Y^GXX8:GYY8:US2:9800:9000:9600:9900hCL$:9600:Z$(1)"LARGE":Z$(2)"MEDIUM":Z$(3)"SMALL":CO:"So for the"::"3 x 3 grid,"::"there are"rCC,0:I311:X40:Y150I10:CO,X32,Y:ZZ4I:Z$(]@X110:Y50:GS3:CO,20,120:"Now consider a grid 3 units"::"on a side.":9600:C0:9000J9100:CO,20,120:"There are now 9 small squares"::"(size 1 x 1) and 1 large square"::"(size 3 x 3).":9000*T9100:CO,20,120:"There are also some med0:"There are 4 small squares"::"(size 1 x 1) and 1 large square"::"(size 2 x 2).":9000 ,9100:CO,20,120:"The total number of squares"::"is 5. (4 + 1 = 5)":C1:9000 6N2:8800:CO:"We will keep track of"::"information on a chart.":9000"::"grid is a 1 x 1 grid.":AFT,4:CO,110,100:CN$"!"CO${ CO,20,140:"Clearly, it contains only 1"::"square.":9000 X110:Y50:GS2:CO,20,120:"Now consider a grid of just"::"2 units on each side. (2 x 2)":9600:C0:9000\ "9100:CO,20,12cult if you can't":CO,45:"think of how to simplify.":CO,45,120:"Seem like a long, slow":CO,45:"way to get the solution." BL38:BR238:BU80:BD108:9200:BU115:BD143:9200:9000: CO:"The simplest case of our"::"original problem of a 5 x 5ed on":CO,45:"a similar problem.":CO,39,120:"Help you see a pattern to":CO,39:"use to solve the problem." BL37:BR231:BU80:BD108:9200:BL31:BR239:BU115:BD143:9200:9000~ CO,10,45:"But simplifying the problem can":CO,45,85:"Be diffiVSP:WIND1 I16:AN(I):I:1,5,14,30,55,917 900,3:MAX100:C1:CO,0,10:CN$"SIMPLIFYING THE PROBLEM"CO$CC$:AFT,3:WL20:WR260:WT20:WB191:WIND,WL,WT,WR,WB:9300o CO,10,50:"The simplifying method can:":CO,45,85:"Help you get startN, SQUARES-SIM(DEVBYLOISEDWARDS:BYR.ERICKSONK((C)MECC1983Qddi230,64:24576n16384:CM$(13):D$CM$(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):3:QU$(34):SS$(1)"s":SS$(2)"is":SS$(3)"are":CC$(3):CO$:AFT,1 x                     r the method"::"you used.":::"Hope you enjoyed the challenge of"::"this problem.":9000:920&RAFT,3:CN$"CONGRATULATIONS"CO$", your method"::"works!":CO,20,100:"That problem took some very good"::"problem solving skills."$'\::"Hope yoCO,W,150:"(You may want to use a worksheet"::"to help you.)":MAX500:CO,X,Y:9700k% CL$:OP385850%*CO:"No, that is not it. The answer"::"is 385 squares in a 10 x 10 grid.":::"Recheck your arithmetic and see"c&4:"if you need to alte METHOD"CO$CC$:AFT,1:$:"to find the number of squares in a"::"6 x 6 grid.":CO,W,120:"Now try this method on a"::"10 x 10 grid.":9000V%CL$:GS10:X100:Y20:9600:CO,W,110:"How many squares are there in a"::"10 x 10 grid?":X120:Y128:CO,X,Y:9700#W0:WIND,W,20,279:9120:CO:OP91įCO,W,10:"No, the number is":CO,W,20:"91 = 1+4+9+16+25+36."CC$:CO,W,30:"There are 91 squares in a 6 x 6":CO,W,40:"grid.":9000$ W5:WIND,W,20,279:CL$:"You have used the"::CN$"SIMPLIFYING0,170,279,191."I6įCO,X8(I4)7,Y:"+"q"I:WIND,20,20,260,191:C0:9000:C1:9120:BOX,20,170,279,191 #VSP,4:CO:"Now add the number in the sum column for the 6 x 6 grid and enter that sum as the total.":VSP::X98:Y152:BOX,X,Y,X32,Y8:orrect."CC$:"Fill in the sum column for the"CC$:"6 x 6 grid."CC$:VSP:Y152:CO,154,Y:9300:WIND:"1+":I26:X138I15(I4)8(I6)8:CO,X,Y:9700 "OPIIįBOX,X,Y,X32,Y8:CO,0,172:CEL:"No, the answer is "II"."CC$:CO,X,Y:II:SPACE:BOX, found to"::"solve a new problem:"::"Determine the number of squares"::"in a 6 x 6 grid.":9000 N5:8800:Y152:CO,20,Y:"6x6":X98:CO:"Enter the total for the 6 x 6"::"grid.":CO,X,Y:9700:OP91900!9120:VSP,4:CO:"No, "OP" is not cttern.":9000CO,W,20:"By now you have found a pattern":"in the simplified cases and have":"seen how it was used to solve the"::"problem.":CO,20,100:"There are 55 squares in"CC$::"a 5 x 5 grid."CC$:9000e CL$:CO:"Now use the pattern youyou have found a pattern in"CC$::"the simplified cases and used"CC$:"it to solve the problem."CC$:::"There are 55 squares in"CC$::"a 5 x 5 grid."CC$:C1:9000:700 N5:8800:CO:"Here is the completed chart,"::"be sure you can see a pathe number in the sum column for the 5 x 5 grid and enter that sum as the total.":CO,98,140:9700:CL$CO:OP55ĺ"No, "OP" is not correct.":::"Perhaps your arithmetic contains"::"a slight mistake.":C1:9000:685GCN$"Good."CO$CC$::"Now I15(I5)7:CO,X,Y:9700:OPIIįBOX,X,Y,X32,Y8:CO,0,172:CEL:"No, the answer is "II"."CC$:CO,X,Y:II" ":SPACE:BOX,0,170,279,191I5įCO,X8(I4)8,Y:"+"I:C0:9000:9120:BOX,0,172,279,191gWIND,10,20,270,191:CO:"Now add metic contained an error or the pattern you saw wasn't quite correct. Let's look again for a pattern.":C1:VSP:9000lN4:8800:Y140:CO:"Now fill in the sum column for"::"a 5 x 5 grid.":CO,20,Y:"5x5":CO,161,Y:"1+"v9300:WIND:I25:X145::"You seem to have good"CC$::"problem solving skills."CC$]:::"You successfully used"CC$::AFT,1:CN$"SIMPLIFYING"CO$CC$::"to solve this problem."CC$:9000:700vbVSP,8:WIND,20,20,260,191:CL$"No, "OP" is not correct. Perhaps your arith30ĺ"No, the total is 30 for a 4 x 4"::"grid.":CO,100,Y:"30 ":900009120:CO:"Now guess the total number"::"of squares for a 5 x 5 grid.":CO,20,140:"5x5":CO,100,140:9700:Z(OP55)(OP55)2:Z600,610>XAFT,3:CL$:CN$"TERRIFIC!"CO$CC$9000BOX,0,0,100,100:CO:"So for the"::"4 x 4 grid"::"there are":60,159210,159:CO,62,162:"30 Total squares":C1:9000H&C0:N3:8800:CO:"Now add this total to the chart.":Y128:CO,20,Y:"4x4":CO,185,Y:Z$:CO,100,Y:9700:9120:CO:OP4 x 4 grid"::"there are":I14:CO,100,110I10:I" x "I" square(s)":Z0:I411:X70(II10)8:Y160I10:CO,X,Y:9700:ZZ(OPII):I:Z4įBOX,0,0,100,100:CO:"Count again."::"There are":I411:CO,70(II10)8,160I10:II" ":: box has a number which represents the area of that":"county.":Z1:X%(1)220:X1%(1)260:Y%(1)20:Y1%(1)60:A%(1)10:C%(1)3:7800:9800:8900:90000TVSP,8:CO,10,100:AFT,3:"The cost of coloring a county"CC$:"on the map is found by"CC$:CN$"MULTIPLY have a common border, so they cannot both be the same color.":9000,W0:WIND,W,20:CL$:"The cost of printing these colored maps depends on the color of the ink used."::"Here are the ink colors and costs:"6X40:Y120:8700:9000:CL$J"Eachcommon border can have the same color."[BL130:BR260:BU77:BD145:9200:9000:BOX,130CO:"Are these two counties colored correctly? ":Z34:C%(Z)3:9800:8800:ZD"CO,222,52:36000:Z$"Y"įBOX,130:CO:"No, look again."::"These counties maps."::"The counties' boundaries are all straight lines, so the counties look like boxes on the map.":9000:CL$'P4:XX20:YY20:W137:WIND,W,20,260,190:7900:9500:CO,W,20:"Your job is to color each of the counties."::"No two counties with a BR140:BU60:BD115:9200:CO,20,160:"Do you want instructions? ";:36000:Z$"N"500 WIND,10,20,270,191:CL$:VSP,8:AFT,3:CO,20,0:CN$"INSTRUCTIONS"CO$CC$t CO,20,40:"You are assisting your state mapping department in producing regional county:7900:CL$:CO,20,0:CN$"THINKING WITH INK"CO$CC$:9500:ZZ13:Z1N:C%(Z)((1)51):9800:Z:ZZ:9000 VSP,2:BOX,0,40,279,191:P1:XX140:YY60:8100:9600:CO,W,68:"A color monitor":"or television is":"needed for this":"program."V BL12:6):L(Z)Z(H(Z)256) 1:0:7:OPEN,"INK.BIN":Z011:AD%(Z),L%(Z):Z: 1301,223,0,60,60,60,120,81,201,60,261,325,586,303,889,250,1138,37,1175,37,1212,53,1264,37 REED,AD%(0),L%(0)AD:LM(AD221)l VSP:W18:WIND,W,20:AFT,1:XX40:YY60:P5150:Z012:CO%(Z):Z: 4,6,25,5,26,15,7,66,82,79,68,80,87g }D%(1)132:D%(2)347:D%(3)341:D%(4)290 CA$(1):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):CP$(16):CC$(3):L$"ONE TWO THREEFOUR HARD " P(Z)(Z)(Z1)256:H(Z)(Z250 THINKINGW/INK(DESBYL.EDWARDS>PROGBYR.ERICKSONL(MECC1983T2:d230,64:24576:16384:X%(34),Y%(34),X1%(34),Y1%(34),C%(34),A%(34),CO%(12),M$(34),SC%(10),AD%(11),L%(11); xAD34590274:XP150:YP90:XD4:YD4:WL35:WR245:WT45:WB                :YD1:WL35:WR245:WT45:WB150:I012:CO%(I):I: 4,6,25,5,26,15,7,66,82,79,68,80,87:D%(1)132:D%(2)347:D%(3)341:D%(4)290 D$(13)(4):CL$(12):CN$(14):CO$(15):CH$(8):CJ$(10):QU$(34):CP$(16):CC$(3) P(I)(I)(I1)256:H(I20,279,50:OPMSMSįCO,20,20:"No, the correct answer is "MSMS:CO,X,Y:MSMS:9000\+!+!NS0:YX1GSUS1:XY1GSUS1:NSNS1:UXXY:UYYX:CO,218(NS10)7,57:NS:N15:9800:N:XY:YX:+!+"Z51T::+`"%,j"9300:WIND:CL$:10,80" x "US" squares,"::"move the cursor to a square and"::"press SPACE. When you are"::"finished press RETURN.":{*\!*a!QUS1*f!N5:P1:8800:CO,20,20:"Now fill in that number on the"::"chart."V+p!X188(MSMS10)7:Y90Q10:9700:BOX,20,O,40,20:AFT,4:CN$;","CJ$;CH$"("CJ$CH$CH$CH$"%) *$"CJ$CH$CH$CH$"+"CJ$CH$"-"CO$)M!CO,195,10:"Number of":CO,209,20:US" x "US:CO,202,30:"squares":BL208:BR238:BU50:BD70:9200:BOX,217,57,230,66u*R!W10:WIND,W,W:9100:CO,W,120:"To count the "US number of squares in a 10 x 10 grid.":VSP:9000L(5000:RNH,"SQUARES-B"x(CL$:CO,0,90:"One moment please...":~(@(4!(>!9100:CO,W,120:"Look again. You have already"::"counted that square.":9000:O)H!:CO,10,10:"To move cursor":Cu enjoyed the challenge.":9000:920'WIND,10,20,270,191:VSP,8:AFT,1:CL$CN$"GREAT!"CO$CC$:"You found the answer by using the pattern. That's a lot easier than counting all those 91 squares."1(:"You might want to use the pattern figure out thean":CO,W,40:" 1. See the lowest possible":" cost map": %" 2. Color a different practice":" map"::" 3. Color a large map"::" 4. Stop for now":CO,20,140:"Which do you choose?" *X184:Y140:MA4:9700:OP820,700,530,630BL20:BR279:BU0:BD191:WIND,BL,BU,BR,BD:CL$:VSP,4:CO,20,91:"Do you want to try another practice map? ";:36000:Z$"Y"700!H800!CL$:CO,0,90:"One moment please...":w"L912266,80:58,6058,170:150,60150,170,t"HSP,1:CO,7,60:"Size of":CO,65,60:"Total number":CO,14,70:"Grid":CO,73,70:"of squares":CO,203,70:"Sum":HSP,2#-~"Z$"1":ZZ1N:Y80ZZ12:CO,20,Y:ZZ"x"ZZ:CO,106(AN(ZZ)10)8,Y:AN(ZZ):CO,2098ZZ,Y0 9000:BOX,0,YT5,279,191:L6:W4:8400 CO,20,120:"This table has a base of 6 units and a height of 4 units.":CO,XR32,YT16:"Base: 6":CO,XR32,YT32:"Height: 4":8300:9000y AFT,3:BOX,0,120,279,191:CO,20,130:"You can change the dimen"500r B0:VSP,1:AFT,4:CL$"You will be working with"CC$::"rectangular pool tables."CC$:L3:W5:8400:9000 CO,20,120:"This table has a base of 3 units and a height of 5 units.":CO,XR32,YT16:"Base: 3":CO,XR32,YT32:"Height: 5":8300*DEFG"CO$* L%(48),W%(48),B%(48),P%(48)4 8000: AFT,4:WIND,20,20:XC130:L12:W8:8400:PIC1:8200:PIC0:CO,XL23,70:RACK$ CO,10,10:AFT,1:CN$"POOLING AROUND"CO$CC$:AFT,1 CO,20,160:"Do you want instructions? ";:36000:Z$"N(I(10P).5)10P:P0:RA(I)((1)I):CL(I)(IZ)6 XD(1)16:YD(1)4:XD(2)6:YD(2)4:XD(3)3:YD(3)4:XD(4)3:YD(4)12 1:0:3:SPD3:TRY0 RACK$CN$"89:;"CJ$CH$CH$CH$CH$"<=>?"CJ$CH$CH$CH$CH$"@ABC"CJ$CH$CH$CH$CH$"A x 3 grid,"::"there are"rCC,0:I311:X40:Y150I10:CO,X32,Y:ZZ4I:Z$(I)" squares ("ZZ" x "ZZ")":CO,X,Y:9700:OPIIįCO,20,170:"No, the answer is "II"."CC$:CO,X,Y:II" ":9000:CO,20,170:CEL:wI:CO,20,180:CEL(|30,150220, ( (((( <((( (8<((D(  (((<(P< <( (( (< <( <<( (((<2((((NH,"MENU"r7}CL$:CO,0,89:"One moment please...":(4)"BRUN Y2UTIL.OBJ":RNH,"PPRINT.OBJ":RNH,"THINKING W/INK"}7154367DB:GCP,ZX,ZY7BL(771):BR(772)(773)256BL1:BU(774):BD(775)1F8WIND:CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$WRXPXPXD:9920=6&(CH77CH10)YPYDWBYPYPYD:9920Z6&Z16:CHCO%(Z6)COZq6&CH48ZXDZ:YDZ6&Z:CH81CO0ı6'99206yWIND:VSP:CLOSE:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"32000 7,yZ$"N"İ5000:R2,CO%(C%(Z)):85&CO0:CC16368:CI16384:CJ128:CI,05&2XP,YP3:CC,0:CI,CJ:CH(CI)CJ((CI)128):CH96CH122CHCH325&2XP,YP35&(CH73CH11)YPYDWTYPYPYD:99205&(CH74CH8)XPXDWLXPXPXD:99206&(CH75CH21)XPXD0::&4%Z1N:7800:9800:8900::4%:CO,X,Y:INP,(((MA)),N),Y$:OP((Y$)):OP1OP(MA)įWIND:CO,5,182:"Enter a number from 1 to "MA" please.":WIND,W,20:97004%BOX,0,182,279,191:CO,5,182:CEL:5H&BOX,X%(Z)2,Y%(Z)2,X1%(Z)2,Y1%(Z)UZZ:BLZZ,BDZZ:BRZZ,BDZZ:7:3T$WIND:CO,X,Y:INP,(3,"YESNO"),Y$:Y$(Y$,1):Y$"Y"Y$"N"įCO,20,182:"Type in yes or no please.":93003h$CO,0,182:CEL:3%Z1N:7800::30%TT0İ9620:3:%Z1N:7800:8900::4%Z1N:7800:980CP$A%(Z):VSP,4:HSP:*2(#CA$:SPACE::C2#BOX,0,137,279,191:\2#BOX,0,145,279,191:2#Z0:Z13:2:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZ#3$ZZZ11:BLZZ,BUZZ:BRZZ,BZ1(Z110)10(Z110)10(Z17)3x1t"ZZ12:CO%(C%(Z))Z2:9800:ZL1100:ZL:CO%(C%(Z))Z1:9800:ZL1100:ZL:ZZ1~"CO%(C%(Z))Z1:8900:2"HSP,0:VSP,0::ZL((A%(Z)))5:BOX,X1%(Z)ZL2,Y1%(Z)9,X1%(Z)3,Y1%(Z)2,4:CO,X1%(Z)ZL3,Y1%(Z)9:X:(CL(XR)CL(XL))8590->!CL(XR)8550HH!ZY:CL(YT)P4:8580_R!CL(YB)P1:8580i\!8590f!ZY:CL(YT)P3:8580p!CL(YB)P2:8580z!8590!SNK1:SOUNDāI10505:PLAY,I,5:!!!YDYD:8500:SNK8640.!BB1:,IXR2,I:I   SNK0:XLXCL6:XRXCL6:YT86W5.25:YB86W5.25:OXXL:OYYB:PXXL:PYYB:XXL:YYB:XDSPD:YDSPD.875 BOX,XL,YT,XR,YB,1:BOX,XL,YT,XR,YB,30 I01:XLI,YTXRI,YTXRI,YBXLI,YBXLI,YT:I 4!9!SNK0:Z,XL1,YT1:CN$"0":CO,XR8,YT1:"1":CO,XL1,YB8:".":CO,XR8,YB8:"/"CO$ PICįCO,XL9,YT9:"D":CO,XR9,YT9:"C":CO,XL9,YB9:"A":CO,XR9,YB9:"B"& l v IXLXR12:I,YT2I,YT:I,YB2I,YB:I  IYTYB10.5:XL2,IXL,I:XR1,22334590274:SOUND((34812274)):CLOSE:5d1X,Y:PXOX:PYOY:OXX:OYY:XXXD:YYYDyXXLS1:8700XXRS2:8700YYBS3:8600YYTS4:8600PICBPIC1ı1OX,OY:PX,PY:SNKı8110 N :COom other pool tables? ";:36000:Z$"Y"510bCL$:CO,20,70:"Now write some rules to predict the number of bounces and the final pocket for any size pool table.":9000l31000CL$:CO,0,90:"One moment please...":/@OPEN,"INK.BIN":REED,1308800:TRY48600NW5:WIND,W,20:CL$"You have tried 48 different pool tables. The data chart is filled.":CO,W,100:"Do you want to start again? ";:36000:Z$"Y"TRY0:510+XWIND,20,20:CL$:CO,20,100:"Do you want to continue collecting data frCO,10,184:"press the SPACE BAR.":16368,0:16384,128:16368,00BOX,0,YB17,279,191:CO,XR24,80:"Bounces":CO,XR34,108:"Final":CO,XR30,116:"Pocket":8100:CO,XR48,129:(64P):9000DTRYTRY1:L%(TRY)L:W%(TRY)W:B%(TRY)B:P%(TRY)P:ND4MIN2:MAX15:X50:Y60:Z$"Base: ":9700:LOPi MIN2:MAX14:X50:Y80:Z$"Height : ":9700:WOPCL$:8400:8300:8200:CO,XR34,20:"Base":CO,XR44,29:L:CO,XR30,50:"Height":CO,XR44,59:WB&CO,10,176:"When you are ready to shoot,":20,70:"Before you begin to experiment with the pool tables, would you like to read the instructions again? ";:36000:Z$"Y"235WIND:VSP,8:8900:CL$XC110:B0:VSP,8:AFT,4:WIND,20,20:CL$;"Enter the dimensions for the pool table.":WIball.":9000CL$:AFT,1:CO,20,40:"You may want to use one or more of these strategies:"CN$:CO,73,90:"Trial and error":CO,59,110:"Exhaustive listing":CO,37,130:"Simplifying the problem"CO$BU85:BL33:BR270:BD150:9200:9000CL$:CO,0,120:QU$"Pool around"QU$" with the base and height and see what ":CN$"PATTERNS"CO$" you can discover.":9000 CL$::"Make a "CN$"CHART"CO$" to keep track of your results.":CO,20,110:"Try to "CN$"PREDICT"CO$" what will happen before you shoot the 14:8100:PIC:PIC0LrCO,20,140:"This ball falls into pocket D.":9000CL$:"The number of bounces and"CC$::"the pocket change as"CC$::"the pool table dimensions"CC$::"change."CC$BL34:BR245:BU20:BD100:9200oAFT,3:VSP,8:CO,224:8100:PIC:PIC0^CO,20,140:"This ball bounced three times.":X10::Y160:Z$"Which pocket did it fall into? ":M$"D":9800:Y$"D"įCO,XR20,80:AFT,1:CN$"Right!"CO$:9000:400hCL$;"No, watch the ball again.":B0:PIC0:8400:8300:8200:PIC.":PIC1:8100p@CO,20,140:"When the ball hits a side of the table, it rebounds at a 45 degree angle.":9000JBOX,0,0,279,YT12:BOX,0,YB20,279,191:BOX,XR12,YT,279,YBTCO,20,20:"The ball continues moving until it falls into a pocket.":PICre labeled as shown.":8200:9000"CO,20,130:"Only one ball is used here. The ball will always be shot from corner A.":9000,BOX,0,0,279,YT12:BOX,0,YB20,279,191:BOX,XR12,YT,279,YB6CO,20,20:"The ball is always shot at a 45 degree anglesions. The "CN$"BASE"CO$" can be any whole number from 2 to 15. The "CN$"HEIGHT"CO$" can be from 2 to 14.":9000:AFT,4 BOX,0,0,279,YT12:BOX,0,YB20,279,191:BOX,XR12,YT,279,YB!CO,20,20:"Each corner of the table has a pocket. The pockets aL2f -`,f`'im(imʈ*i+i)iʎ,iL6i Kggg`gg ggg`g Kg gggg`ggg8pg.g(gggmgg`8pgJJJ) }gggmgg`((((PPPL de80 " Tfm8h)` dem88eLf` deme` d8` f@ f f f`Lc dff`) ``fʽ`) ` `fH`mS` dS`)ae``e hae g`e}`mf8ff`f` dLc,0*`%f 8fHfJhj`mfff` c d` c dI``f`emfff`) ffffffO,0 `)  d`f(`HHf,Pf88`f d fhLcfHfHff,P d fhf8hfffffff``S`S```f穀f f`f3f'ff `ɀ   LX8e湥 qHqH L`@ @ʩ WRPT` J  dȱȱȱ` hfH) #,f h`` fffffffh`f fS```emffff  2f%%h $20 LZc $ aHaH`daemeWeeeef1fSflffffff(bb d (cf hf gNOH (c h f ghH ,aɈ.hH (cb h) e f g (c fbbh`˅o 8````L`bbbbIq$% `@ GaLa6 ,fLcLmfPa bHaa,aaɠ,wa ` a欇aah`ɀ)?  @IH (c$ d f$%0 dL: PPPPPPPP pp(p  @@@h @ @ @ p pK$yVSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"Ĭi$,yZ$"N"İ5000:RNH,"MENU"|$DB:GCP,ZX,ZY$CO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020%CO,0,182:CE((Y$)):OPMINOPMAXįCO,10,182:"Enter a number from "MIN" to "MAX" please.":9710l#%CO,10,170:CEW:r#H&#R&CO,X,Y:Z$;:INP,(1,A),Y$:Y$"A"Y$M$įCO,10,182:HSP,1:"Enter a letter from A to "M$" please."CC$:HSP,2:9810$\&CO,10,182:CEL:"#"#Z0:Z13:5:ZZZ101:BLZZ,BUZBRZZ,BUZ:BRZ,BUZZBRZ,BDZZ:BRZZ,BDZBLZZ,BDZ:BLZ,BDZZBLZ,BUZZ:ZZ1:ZZ"$ZZZ11:BLZZ,BUZZ:BRZZ,BUZZ:BLZZ,BDZZ:BRZZ,BDZZ:3:"%V#%CO,X,Y:Z$;:INP,(((MAX)),N),Y$:OP0,40:"Use these patterns to"CC$:CN$"PREDICT"CO$CC$:"the number of bounces"CC$!""and"CC$:"the final pocket"CC$:"for "CN$"ANY"CO$" size pool table."CC$:9000:!(#CA$:SPACE:!<#C1ĺCL$!F#!# "#BOX,110,15,270,115:BOX,10,115,260,180:" "AFT,3:CL$;"Here is the problem":CO,0,40:"Find a "CN$"PATTERN"CO$" that"CC$:"relates the pool table"CC$:"dimensions to the"CC$ ""number of bounces"CC$:"and to the"CC$:"final pocket."CC$:BL30:BR240:BU20:BD150:9200:9000P!"CL$:CO,616:KK1:YK930:CO,28,Y:L%(J):CO,98,Y:W%(J):CO,174,Y:B%(J):CO,238,Y:(64P%(J)):J:SPACE:BOX,0,30,279,191:I"MK0:IN161N16M:KK1:YK930:CO,28,Y:L%(I):CO,98,Y:W%(I):CO,174,Y:B%(I):CO,238,Y:(64P%(I)):I:SPACE" j"CL$:CO,123,0:"CHART":CO,228,11:"Final":CO,22,20:"Base":CO,88,20:"Height":CO,159,20:"Bounces":CO,224,20:"Pocket"t"22,2948,29:88,29131,29:159,29208,29:224,29266,29:N(TRY16):MTRYN16:N8840z~"I0N1:K0:J(I16)1I1CO,XXD(S),YYD(S):B:PICįCO,XR44,89:B" "D!SOUNDįPLAY,30,2J!P!k"XDXD:8500:SNK8740"BB1:CO,XXD(S),YYD(S):B:PICįCO,XR44,89:B" ""SOUNDįPLAY,30,2$"."BB1:CO,XXD(S),YYD(S):B:PICįCO,XR44,89:B" "`"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020N7CO,0,182:CEL: PPPPPPPP pp(p  @@@h @ @ @ p ppD`````lxx|| |x ````l8|x0x0x| x0`0````0``0``v000xx x000000xx0x0xx0000 0``0 pp pp`0x |||| ||x|8l````|| x````8pxx|| |x ````l8|x0x0x| x0`0````0``0``v000xxxlxx x000000xx0x0xx0000 0``0 0x`0x |||| ||x|8l````|| x````8p`````l 0`xx0p0000xx 8` 8 x8x x<`x 0```xxxx| ```0``0`00`x000||0xxx||````` x@[`{~ @BOHOOUNHOOCECRDFAFPARSNOJUSJUSCNNOCNGCDVSHSSPACCEPAUSCWININjymmfkUkxkkkkkkkdkk#lmcmmm n`lllll~~~0` pvv0`0``0`000`~<~0000`` ɛ MBpBp0LDpBpɈTPɿɯ,p 詍0@ɍp7,p pCp) }pCp9p Џ pLo ` ֩PyQ AL }ppp`uptp Uptpup` ~L_pH)hJJJp`LANCS AZ09!/:p-͂ooo _pLnõoo^`No ݤp 輤pppp߹ppo _po , g 掏p ,o vpp) p pp)p ߅ l o ) L{Bp HHHp hhh `+ hR("  h5880`L pppop ( vpLRo Ln {$0! 掐p ,L)o k {$0L#oNo 千oLoo n|-?npLn Up no n U mhhhhhhhhh,lp` ֩PyQ ALŠҠ僁'i(imiʈ*i+i &')iq&,iL6i N8`f `.f`mm ` ң Σ  h @)`,` sj ެLqj,Hl  !l  h!l`L, HHHHHHHHH k l jlNO,ɍɠ ɛ8nl,lPݩ'i(i)i hmHihʍ*i+i,i L8iL Sk TkMUkSk &g<>=MUk?'<>SkSkTk` H g Rh PQ`L     խ)?` `& ,jQ&-0iQ&&)i)i,i`/i-0i/i)i &g&'-i ,jQ&-/iQ&&)i)i,i`*U U*ժ gj')JMgj)1i Q&,5iP 0=lj`hj`J&)` `L3f̙jj ߅$0Hjj LbLvjj j` hH)8 qȥq8)h` g R  QP (`L h`L)  @ 5ij1i3i j2i4i'i(i g-i j/i*i+i g.ij0i-i.iB)i &g&'-i ,jQ&-/iQ&&ȭ1i.i ,jPhHhhh hJ` &eeieh ghIiwhi 썼h &gmh﬽hMhwhPjjjjjjj0jj) h0ȱjhjhhУ`8pP     choose? ":MIN1:MAX3:X190:Y150:9700< OP800,700,990B  WIND:CL$CN$"POOLING AROUND"CO$CC$::"Management Options"CC$::WIND,20,20:VSP,5:SO$(0)"OFF":SO$(1)"ON":8300F CO,20,60:"The "CN$"SOUND"CO$" of the ball bouncing against pool CO,20,35:"The options include":WIND,30,20:CO,20,50: "1. THINKING WITH INK-":" change map outline or":" erase TOP TEN scores": "2. POOLING AROUND-":" turn sound on or off": "3. Return to main menu"( CO,20,150:"Which do you)(I256):L(I)I(H(I)256) 1:0:7:OPEN,"INK.BIN":I011:AD%(I),L%(I):I:1301,223,0,60,60,60,120,81,201,60,261,325,586,303,889,250,1138,37,1175,37,1212,53,1264,37 8300:AFT,3 VSP:WIND:CL$::CO:"Management Options"CC$7 3CCnJ*NAsBc600`CFJUOAs``wBfgC{9{{ J*B MBlLC8W0W8JUBBgBlgC {{ J*BBC AC~}~}~JUwJUNGY DyjGsBBCFB;FJ*NGY LL |hGsB`B0`Ca]a}}JUNGYd`gg`dg`phGsBgB0gC.5B;J*NGAGsBsB63Cwx{JUNGAGsBs600p00CBnJ*NGAGsBcB6cCtwutJUNGAGsBsB6BX}- CFJ*NGYxpBspxBAOGGBOA]GOH@NHxBByB{CFJUNGVApEsA@EOO]GsBBqCFJ*NGYCsgEp`g``p]Gs00{C3ACFJUNGYCy|>?Ex]GsvC6ACFJ*NGVAyxxByA`F~~~^GsBcB6f`CBCFJ*NGY~| B|CAyA`ByC]GOG|L|HBFACFJUNG[A`Hss]GOD@CAAGA <B~BBBYCFJUNGY!DIE20Bspr]GQF@`Dp`@HB@@_BY_J*NGYCFJ*NGAGO?_WUUUBUABUCUBB>0CFJUNGTvGJ??C*B*B***B*AB*C*Bt u@ )` t t t0H)?hJ t t t?Lt t&'&Ȅ``tt ttt`t)tJJ tttt .t .t ntt)xxx| ```0``0`00`x000@@0xxx||````` xxxxlt(` lllll~~~0` 0`0``0`000`~~0000`` 0`xx0p0000xx 8` 8 x8x x<`x 0```x ` 008|88888888|8UWX````XWU `l8|x0lx0x| x0`8x``x800000000pxxp(000xx0x0xx0000`p80x`0 x ||xx ||x|8l````x| x00000 xp00000xlxx|| |x ``` x8`x 000xxxx| |x888888808p8||||p88px00xxxxx000 xxxxtxx x00TTTT`888888ll$lHHH0 0<\`@ Tt0008ppp8p88pT8|8T000080||888pxx>gccccg>>~~ug` fffffffffl6iɆpqs 0 000000 0 0Z<|~~6<0>?`LvLvLv>?`L*vø{{ttlnghab\\WWRRMNIIEEAA=>::673401..+,))&'$%"# ! 3#< = <=Lu <=LuLPLAv`~uL+usutu+uLvɯtu 8ɀ   Lޤȱ:,Әe湥 vHvH L`sutuL ,v -v8,v?=4=0>?`LuLu  @ @ p p $"RUN DIAGONALS-EXH"aCL$:CEW:CO,0,90:"One moment please...":g(#y2#CA$:SPACE:<#CL1ĺCL$F###BOX,110,15,279,115:BOX,10,115,260,180::#L#5:Z0:ZB3:ZZZB01:BLZZ,BUZBRZZ,BUZ:B%,yZ$"N"Ĺ900,0:5000:RNH,"MENU"+>DB:GCP,ZX,ZYCO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020CO,0,182:CEL: PPPPPPPP pp(p  @@@h @999))1)16:BS1BS7BS6# }BS `` `@@@@`@ )C<<>..,#$#$66.)-??LI$$,ۅ3@ @ @@@`@````ࠠ@@@` @ࠠ@@@``@ @@@@@@@ࠠ@@@@ @`@@@`@ @@@@@ ```` ``@` @@@``@@ ` @@@ࠠ@@TDT`@@@@@``@ @@ @ @ @@@ @@@@@@@@ @@@@@@@ @ @ ` `@ @@@@@@` @@@@ @@ @@@@@@ ʪn{.uյ*ruJ\vۻwvr*vJjʪ `,X` {ݩD ^ D` &Ls`L 䎱 掲`RFRNSEOPEREEWRITCLOS? 鎰:p";>? Ўp F 8`L_8ghgmihmj8Btv w vw8vw8>? Ў9p!>? Ў&pg^h_^`ȱ^  ` j-`- { 媤^_ ` L ׌ ` ׌ ` j` - `L { RPQ { RPQ { RPQ`  { RPvQw L xLl` x& eL׭vqwrXvwLXLXv<<`<=< -   ) 8 -`- 8`X^_ ^-\]`a X  ` ʀ-LL 8ɀ  L8e湥 HH L` <=<ȥ?< <<= H <=I     RA(I)((1)I) 31 (900)0(900)4275T WIND,10,10:AFT,4:CN$:900,0f M511:Z0 NRA(5):S(M,N)210 S(M,N)1:X113M8:Y70N8:XX0:YYRA(192):XS(XXX)20:YS(YYY)20L OX0:OY0:I118:CO,OX,OY:" ":XXXXXS:YYYY   ,yZ$"N"İ5000:RNH,"MENU"%8DB:GCP,ZX,ZYCO,ZX,ZY:CEL:INP,(3,"YESNO"),Z$:Z$(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020CO,0,182:CEL: PPPPPPPP pp(p  @@@h @0:: %%CO,X,Y:INP,(((MAX)),N),Y$:OP((Y$)):OP1OPMAXįWIND:CO,10,182:"Enter a number from 1 to "MAX" please.":WIND,20,20:9710%CO,10,182:CEL:y"yCLOSE:VSP:CL$CO$:CO,0,90:"Do you want to try again? ";:36000:Z$"Y"t Options"CC$::WIND,20,20:#""HSP,0:VSP,0::ZL((A%(Z)))5:BOX,X1%(Z)ZL1,Y1%(Z)9,X1%(Z)2,Y1%(Z)2,4:CO,X1%(Z)ZL2,Y1%(Z)9:CP$A%(Z):VSP,4:HSP:(#2#:SPACE<#CL1ĺCL$F#%&%Z1N:7800::0%Z1N:7800:890n enables you to select one of these maps for the students to color. A "; QU$"TOP TEN"QU$" list of players with the best (lowest) scores is kept for the map you choose.":9000:VSP:4!>!WIND:VSP:CL$CN$"THINKING WITH INK"CO$CC$::"Managemen:AAADZ22:AA,255:AA1,127:ZZ120:AAZZ1,32:ZZ:ZVD WRITE,AD%(0),L%(0)AD:\l v REED,AD%(0),L%(0)AD:LMAP(AD221):SOUND((AD222)):  8500:VSP,5J :"This program contains three different large map outlines. This optioAAADZ22:N$(Z)"":SC%(Z)P(AA):ZZAA2AA21:N$(Z)N$(Z)((ZZ)):ZZ:Z& CL$"TOP TEN LIST"CC$:"Map #"(LMAP4)CC$::Z09::CO,10,Z1240:3((Z1)));Z1;". ";N$(Z):SC%(Z)32767įCO,200,Z1240:SC%(Z)0 Z:SPACE:WIND,20,20:9: Z09M$(Z)"":ZZ1NA:M$(Z)M$(Z)((AA5ZZ)):ZZKAAAANA5:C%(Z)0:Z:Q@lJZ$"ONE":P2Z$"TWO"TP3Z$"THREE"^P4Z$"FOUR"hP4Z$"HARD"rAFT,3:CO,0,5:"Level "CN$Z$CO$:  VSP,8:WIND:CO:8300:AAADL Z09:,Y%(Z)1X1%(Z)1,Y1%(Z)1X%(Z)1,Y1%(Z)1X%(Z)1,Y%(Z)1:ChAAADDRESS:REED,AD%(P),L%(P)AD{N(AA):Z1NX%(Z)XX(AA1):Y%(Z)YY(AA2)X1%(Z)(AA3)X%(Z):Y1%(Z)(AA4)Y%(Z):A%(Z)(((AA3)6)((AA4)6))/NA(AA5):ames from the TOP TEN LIST? ";:36000:Z$"Y"İ8250AVSP:810Gk5000:WRITE:CLOSE:RNH,"MENU"CL$:CO,0,90:"One moment please...":xX%(Z),Y%(Z)X1%(Z),Y%(Z)X1%(Z),Y1%(Z)X%(Z),Y1%(Z)X%(Z),Y%(Z)=X%(Z)1,Y%(Z)1X1%(Z)110qBOX,0,130,279,191:CO,30,140:"Which map outline do you want to use (1-3)?":X165:Y152:MAX3:MIN1:9700LMAPOP4:AD221,LMAP:WRITE,AD%(0),L%(0)AD:WRITE:8250:8103VSP,4:WIND,30,20:CL$::CO,30,80:"Do you want to erase the nThere are three different map outlines. Choosing a different map automatically erases the players' names on the TOP TEN LIST."::"Map "LMAP4" is currently being used."CO,30,140:"Are you sure you want to choose a different map? ";:36000:Z$"N"8Return to the menu"YpCO,20,170:"Which do you choose? ":MIN1:MAX5:X182:Y170:9700uzOP950,960,970,980,210{5000:8200:8105000:8300:XX40:YY50:PLMAP:7900:CL$:9520:9000:810WIND,30,20,279:VSP,4:CL$::""1. View the current TOP TEN":" list of names":]H"2. View the current map outline":R"3. Choose a different map and":" erase the current TOP TEN":" list":\"4. Keep the same map and erase":" the current TOP TEN list":f"5. table walls and falling into the pocket is now"::CN$SO$(SOUND)CO$CC$ CO,0,140:"Do you want to change this? ";:36000:Z$"Y"ĹAD222,SOUND:8260:WRITE 210  %8400 *8500:VSP 4CO,20,30:"You can":WIND,30,20,2794>CO,30,45:4,A4:DFT,5,A57233,(A6256):232,A6(A6256)256=. A management option controls the sound.",""GH::(4)"MAXFILES3"b\P(I)(I)(I1)256pTE274:A0P(784):A130136TE:A231296TE:A332264TE:A433296TE:A534072TE:A634520TEzRFL,"FONTS.BIN"A1DFT,1,A1:DFT,2,A2:DFT,3,A3:DFT,monitor is required. ","FÃ"Pooling Around","POOLING AROUND".Ã"A simulation of one-ball pool tables of varying sizes that enables you to discover patterns by collecting data on the number of bounces the ball takes and the pocket it falls intorid.",""3xà "Thinking With Ink","THINKING W/INK"yÃ"An application of strategies in a game activity of coloring a pattern of rectangles at a minimal cost. A TOP TEN list of scores is kept. A management option allows choice of map pattern. A color al and error, exhaustive listing, and simplifying the problem, to find the number of diagonals in a twelve-sided figure.",""nà "Squares","SQUARES-B","An interactive tutorial on applying any of three strategies to find the number of squares in a 5 x 5 gor #"ZE" in line #"ZN:30000:}2}:"Error #"ZE" in line #"ZN" in Menu Program. Please report this error to MECC.":30000:d}" Please check your disk drive and diskette.":30000:|dÃ"Diagonals","DIAGONALS-B","A tutorial on using 3 strategies: tri6384):ZL(Z127)::ZZ128:16368,0:,0u=:u:SPACE::LyCL$:2020y}ZE(222):ZN(218)(219)256:ZE255Ĭ}CO$CL$:WIND:HSP:VSP:CO,0,80:ZE6ĺ"Error: File not found.";:32100}ZE8ĺ"I/O Error.";:32100(}ZE0ZE16ĺ"DOS ErrX,ZY:WIND,ZX,ZY,250,ZY12:DL$(127)L2#DL$:CO,ZX,ZY:9100:AZ:A19070d<#A49A(48N)9010wF#(A);DL$;CA$;P#9100:Z139070Z#Z8Z127įCO,ZX,ZY:CEL:9010d#9040n#AA48:A1A1x#XX(XX)#:&#ZL11:XX(1):Z(1D4VSP,4:CL$:::"Use of ESC Key"CC$::"You may want to quit in the middle of a program. If so, press the ESC (escape) key twice whenever the computer is waiting for you to type."WIND:VSP:30000:(#%-#CA$;:16368,0:GCP,Z(Z$,1):Z$"Y"Z$"N"įCO,20,182:"Type in yes or no please.":36020m8CO,0,182:CEL:WIND,BL,BU,BR,BD: PPPPPPPP pp(p  @@@h @ @ @ p pP @ @ p p @ @ p pD @ @ p pA(((((%JOHN HOGG BARBARA CATHERINE BARB MELISSA      !,X1%(Z)` ( l (DH<H|0 0|     040( 0 @ $0@$0,(( <((( (8<((D(  (((<(P<<((((<<(<<((((<2`(xx       t8H $ 4 $ (  (  (  $( 4(((H(<8  (, 8, H,  T,  (8,   `  `  44 $ $  $ 4 ! 4  "4 ! $ $ 04 DD D (D 4@ 40 4  $  $ 4 $, PD( D8  P8 h8 `(4(" ,<LD< <,      0  ,  <  L\ `  `  `  `0 `@  `L pH$p8p(p$(  !"( L44Which number?":9700:2060,OP:OP7000,7010,7020,295= #290T '900,0:RNH,"MENU" ,C1:9020:GS5:X120:Y70:9600:CO,20,146:"How many squares do you see in"::Y162:CO,20,Y:"this figure?":X114:MAX100:MIN0:9700:PL(OP1)6@9020:Z(OP26)oose"::"any one of them now and others"::"later if you wish.": :AFT,3:CN$" 1. TRIAL AND ERROR"::" 2. EXHAUSTIVE LISTING"::" 3. SIMPLIFYING THE PROBLEM"CO$::"or "CN$"4. Return to the menu"CO$4 "Y171:X128:MAX4:MIN1::CO,20,Y:"Remember that the question is...":CO,10,136:CN$"How many squares are"CC$:"there in this grid?"CO$CC$ BL35:BR248:BU130:BD166:9200:CL1:9000C VSP,2:W0:WIND,W,W:CL$:"These three strategies may help you"::"solve this problem. You can chYS:CO,XX,YY:"#":OXXX:OYYY:I:CO,OX,OY:" ":CO,X,Y:"#":ZZ1:Z5210Z M:AFT,1 CO,0,10:" SQUARES"CO$CC$:CO,20,140:"Have you tried this program"::CO,20:"before? ";:36000:Z$"N"300g BOX,0,0,279,65:BOX,0,120,279,190:CO,10,40:"0":DFT,6,36790( sAFT,1,0:CO$:VSP,1 xR(I)(I(10P).5)10P:P0:H(I)((228)I)0((228)0)I:LE$"IHGFEDCBALKJ":MM$"M":Z$"DIAGONALS-":Z$(2)Z$"T&E":Z$(3)Z$"EXH":Z$(4)Z$"SIM" SH06:SX(SH,12):PXY0SX(SH,12)1:SX(SH,PXY),SY(SH62 PROG.DIAGONALS-B/DEVELOPERL.EDWARDSIPROGRAMMERR.ERICKSONU(CR1983i2 LM84/09/25EJGui230,64n16384:SX(6,12),SY(6,12),X(12),Y(12):D$(13)(4):CL$(12):CN$(14):CO$(15):CA$(1):CC$(3) pD$"BLOAD ASCII BOLD.PFT,A3679  !!! ! ! ! ! !!!!!!!!!                     D DIAGONALS-T&E(DEVBYL.EDWARDS:BYR.ERICKSONK((C)MECC1983_2 LM84/09/14PWHrd230,64:24576n16384:SX(6,12),SY(6,12),X(20),Y(20):D$(13)(4):CL$(12):CN$(14):CO$(15):3:CC$(3)sAFT,1,0:CO$4 xH(I)((228)I)0( """ " " " " """""""""  tting "F1$"...":216,0:RNH,F2$% Q CL$:11:"Insert another diskette."CC$a 30000:CL$| CS(P(P(999))1)16 CS1CS7CS6 CS  p z4:21,021,191/ 1:9,69,33:11,611,32:9,1589,185:11,15911,185:267,6267,32::GCP,ZX,ZY:ZY160įCO,ZX,ZY4B "Which number? ";:9000:WINDZ AS(1)İ7000:2000 AS(2)A1F1$"the management options":F2$"TEACHER OPTIONS" AS(6)5000 16384 A0ANPF1$MN$(A):F2$CN$(A) CL$:HSP:VSP:CO,0,89:"Ge,MT:CN$TI$CC$:PA$""ĺPA$CC$b CO$:GCP,ZX,ZY:WIND,ML,ZYSP,270:CO:"Program";:NP1ĺ"s"; ":"::L1NP:4(L9):L". "MN$(L):: "Options:": NNP1:4(N9):S(1)N:N". General Information" HNN1:4(N9):S(6)N:N". End" roblem-Solving":PART2$"Strategies":VE$"* * * * *"S jMN$(NP),CN$(NP),DS$(NP,DP) tL1NP:MN$(L),CN$(L):L11DP:DS$(L,L1):: (975)255Č24768:975,1 61000 230,64:24576:DFT,7,15128:AFT,7:CO$:HSP:VSP:WIND CL$:6000:CO,0>  P.S.S.MENU'P.BOUCHARD9((C)MECC,1984L2 84/09/26NAMW15128CA$(1):CC$(3):D$(13)(4):CL$(12):CN$(14):CO$(15)MT13:ML37:SP0P(S)(S)(S1)256RFL,"TITLE.PFT"15128LNP4:DP23 `TITLE$"P  :Z2:Z109000XCL$:Z$LE$:Z0:9540:9530:Z1:9550::VSP,0:CO,125,17:"The vertices of":CO,125:"a geometric figure":CO,125:"are usually named":CO,125:"with letters."IbBL117:BR275:BU12:BD60:9200:11:"In this dodecagon, the"CC$::ain. Remember, a dodecagon"::"has 12 sides and 12 vertices.":CL0:9000:BOX,0,20,279,55:CO:Z$:9800yY$"B"520&BOX,W,20,279,55::CO,W,30:"Oops! You must have miscounted."::"B shows a dodecagon.":Z3:Z103:228,H(127):9530:Z21200:9530:ZY7:2:"A";:7:17:"B":12:2:"C";:12:17:"D":M$"D":9800:Y$"B"530CL$:CO:"That's correct. A dodecagon"::"has 12 sides and 12 vertices."::"This is a dodecagon.":Z6:9540:9530:9000:600iBOX,W,20,279,55:CO:"Try agimagine what a picture"::"of a dodecagon would look like.":::" Think about a clock face,"::" which has 12 numbers.":9000 W10:WIND,W,20,279:VSP,2:AFT,1,6:CO:Z$"Which of these shows a picture of a dodecagon?":Z$:X115:Y31:Z25:95409000w:"Whenever you are working on"CC$::"a problem, try to"CC$:::BOX,75,70,200,85,3:"draw a picture."CC$:BL40:BR236:BU116:BD150:CO,50,125:"A picture can help you"::CO,50,135:"understand the problem.":9200:90005:"Try to e a "CN$"Dodecagon"CO$".":9000:350AFT,1:9020:CN$"Good work!"CO$CC$::"You really know your"CC$::"geometric figures."CC$AFT,3:13:"A "CN$"Dodecagon"CO$" has 12 sides."CC$::"It also has 12 vertices."CC$:BL30:BR250:BU120:BD160:9200:w a shape"CC$::"with 12 sides is called a"CC$::CN$"Dodecagon"CO$CC$:9000:4709020:"The names of geometric figures"::"can be confusing."$BOX,40,75,235,113,3::8:"A dodecagon does not"CC$::"have "(OP)" sides."CC$:::14:"Let's defin:MAX20:CO,20,116:"How many sides does a"::"dodecagon have? "V9700:OP12450AFT,3::CO,20,160:"No, a dodecagon does "CN$"NOT"CO$" have":CO,20,170:OP" sides. Try again.":9700ROP12İ9020:AFT,1:5:CN$"Good!"CO$CC$::"Now you knoon"CO$" helps you remember"CC$::"the number 12."CC$r12:CN$"Do"CO$" means "CN$"2"CO$" (as in duo or dual.)"::CN$"Dec"CO$" means "CN$"10"CO$" (as in decimal.)":9000A9020:"A "CN$"Dodecagon"CO$" is a"CC$::"geometric figure."CC$::Y134:X150s? ";:36000:Z$"Y"400^AFT,3:CL$::"A "CN$"Dodecagon"CO$" is a "CC$::"geometric figure"CC$::"with"CC$::"12 sides"CC$::"and"CC$::"12 vertices."CC$::BL54:BU30:BR220:BD145:9200:90005h"The first part of the word"CC$::CN$"Dodecag9000JAFT,3::"Before you can begin to solve"CC$::"this problem, you must be"CC$::"sure you "CN$"UNDERSTAND"CO$" it."CC$TCO,20,150:AFT,3,6:"(Say d^@dek'@a@gon)"CC$:AFT,3,0:CO,20,120:"Do you know what a "CN$"DODECAGON"CO$:CO,20,136:"iOP300,260,260,260,27055000:D$"RUN"Z$(OP)N5000:D$"RUN HELLO"T,69020:"Here is a question for you:":BL21:BR259:BU52:BD140:9200@CO,45,76:CN$"What is the total":CO,45:"number of diagonals":CO,45:"in a dodecagon? "CO$:e to start at":::" 1. The Beginning"::" 2. The Trial and Error section": " 3. The Exhaustive Listing":" section"::" 4. The Simplifying section"::" 5. Return to the menu"Y156:X188:MAX5:CO,20,Y:"What is your choice? ":9700:0,OP0,165,103,147,93,127,93,110,103,100,120 . 9 24576 W20:WIND,W,W:CL1:9020:3:X50:Y110:N12:L45:9500:9600:9000 "DIAGONALS"CC$:CO,20,120:"Have you used this program"::"before? ";:36000:Z$"N"OP1:250N 9020:"You may choos8,110,216,97,216,83,208,70,195,62,180,62,167,70,160,83,10,40,150,49,162,63,167,77,162,86,150,86,135,77,123,63,118,49,123,40,135,8,157,157,171,171,191,171,205,157,205,137,191,123,171,123,157,137( 12,100,140,110,157,127,167,147,167,165,157,175,140,175,12,PXY):PXY:SH 12,15,70,24,87,42,97,62,97,79,87,89,70,89,50,79,32,62,22,42,22,24,32,15,50,12,15,70,27,91,49,104,74,104,95,91,108,70,108,45,95,23,74,10,49,10,27,23,15,45,6,40,100,62,112,84,100,84,76,62,64,40,76 12,160,97,167,110,180,118,195,118,20und"::"the answer to this problem"::"using "CN$"TRIAL AND ERROR"CO$".":9000AFT,3,0:W15:WIND,W,W:CL$:HSP,2:CN$"TRIAL AND ERROR"CO$" methods can"::"be very time consuming and also"::"can be very frustrating if you"::"can't find a solutihere are fewer"::CO,120:"than "Z2" diagonals."*::CO,120:"There are more"::CO,120:"than "Z1" diagonals.":CO,20,120:"Do you want to make another"::"better guess? ";:36000:Z$"Y"340P4AFT,3,0:CL$:CO,20,40:"You may or may not have fo20:"diagonals.":CL1:9000:340CO,20,40:OP" is a very high guess. Try"::"again.":CO,10,100:"Remember..."::"We decided earlier that there"::"couldn't be more than 108"::"diagonals.":9000:3401 Z0:9540:9530:ZY55:9600:CO,120,20:"T diagonal from vertex"::"A and also a diagonal from"::"vertex D.":CL0:9000:9100 lCO,120,20:"We don't count "CN$"AD"CO$::CO,120:"as different from"::CO,120:CN$"DA"CO$", so there must":AFT,3::CO,120:"be "CN$"FEWER"CO$" than 108"::CO,1"there are fewer than"CC$::(OP)" diagonals."CC$:9000:Z2OP:800XZ0:9540:9530:Z1:9550:CO,120,20:"108 is a good"::CO,120:"guess, but look"::CO,120:"more carefully.":SX(0,8),SY(0,8)SX(0,5),SY(0,5)VbCO,20,120:AFT,2:CN$"AD"CO$" is aere are 54 diagonals."CC$:CL1:9000:900CO,120,20:"Good guess."::CO,120:"However, there's"::CO,120:"room to draw more"::CO,120:"than "OP" diagonals.":ZYOP:Z0:9540:9530:9600:CL1:9000:Z1OP:800CCO,20,80:"Good guess, but"CC$::550:Z0:ZY55:9600:CO,120,30:"How many diagonals"::CO,120:"do you think there"::CO,120:"are?":X156:Y74:9700^CL$:Z(OP53)(OP55OP108)2(OP108)3(OP108)4:Z400,500,600,700)hHSP,2:CO,20,40:"You're a great guesser!"CC$::"ThCL1:9000JW5:WIND,W,W:CO,W,20:"So, to be reasonable, your guesses"::"should be between 0 and 108"::"diagonals.":CO,0,120:"Now you're ready to start"CC$::"guessing."CC$:9000:W20:WIND,W,W:Z10:Z2108wTCL$:Z$LE$:Z0:9540:9530:Z1:9m vertex A."::"There are 12 vertices.":WIND,2,W:BOX,0,120,57,129,3:CO,2,120::"Hint #2": @Z0:Z18:Z2601:9560:Z2:Z211:9560:Z210:9560::"If there were 9 diagonals from":"each vertex, at most there would":"be 9 x 12 = 108 diagonals.":u make your guesses reasonable.",H255:VSP:WIND,W5,W:Z0:9540:9530:Z1:Z$LE$:9550:BOX,18,120,74,129,3:CO,20,120::"Hint #1":::"There are more than 0 diagonals.":CL0:9000:9100_6WIND,110,20,279,191:CO:"There are 9 diagonals"::"fro":::"The computer will then tell"::"you how close your guess is.":9000"WIND,115,5,279,191:VSP,3:CL$:"Since you may not be familiar with trial and error, here are "; '"some hints about how many diagonals there are.":"The hints can help yois the computer"::"program!" ::"(The person who wrote this"::"program knew the correct answer"::"and put it into the program.)":W20:WIND,W,W:9000L::"You will make a guess about"::"how many diagonals there are"::"in the dodecagon. W5:WIND,W,W:::"In this diagonal problem, you"::"can't check your guesses yourself;"::"you'll have to have someone tell"::"you whether your guess is close"::"to the solution.":W10:9000 :"The &someone& that will check"::"your guess 200:9000 W10:WIND,W,W:CO,W:"In some problems, it's easy for"::"you to check a guess yourself to"::"see if it's a solution.":: :"In other problems, you have to"::"ask someone else about the"::"guessed answer.":W20:WIND,W,W:9000,10,27,23,15,45 W20:WIND,W,W:CL1:9020:"Often you start to solve a"::"problem by":CO,63,82:CN$"TRIAL AND ERROR"CO$:CO,20,130:AFT,3:" This is also called a"::" "CN$"GUESS AND CHECK"CO$" method.":AFT,1,6 BL50:BR222:BU75:BD100:9(228)0)I:LE$"IHGFEDCBALKJ":MM$"M":MAX999:MIN0p S01:SX(S,12):I0SX(S,12)1:SX(S,I),SY(S,I):I:S 12,15,70,24,87,42,97,62,97,79,87,89,70,89,50,79,32,62,22,42,22,24,32,15,50,12,15,70,27,91,49,104,74,104,95,91,108,70,108,45,95,23,74,10,49