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C T 6- A6-^11NOW MARK LARGEST EXPONENT, ALSO FILL UP LCMc-}-h''8<,8<,AUmZ8<@, 8<@,668<@,-@ M68<@},-@P'Z Aer>68<@,-@168<@,-@ 4'> Aew |68<@,-@} ?-(8<@,"?68<@,-@ FILL UP LCM MATRIX6--}`8<@,"@668<,-8<,R68<@,-8<@,`6-%@ -}$8<@,@$ Au##NOW INSERT IT IN PROPER PLACE-&@''8<,!8<},Ae-%@6@K'68<,-8&@<,K68<@,-8&@<@, ;}68<,-8<,;68<@,-8<@,6-%@' Au I68<,-8<,;6 }8<@,-8<@,I6-%@ 6-&@$-+@%@ -AV'AV !}6-A;6-P:$H:@,,%@;6-P:$H:@,,%@2-@@2(@find the ofd"}-@@"(@4-@ @E(@W-@@d(@4-@@4(@#}  S-@@0(@ JUST A SEC...4 F-@S(@ A )@$}  B *5-@@5(@ for another4,-@@,(@ to stop>%})@H"@$RAUA! \4-@@##-0(@4 f A T A&})DISCUSSION OF LCM6-A@6-@U +'0@36-@?6-@C '}U@@AV'AV )()( LEAST COMMON MULTIPLE&&( (} 11()The concept of finding a least common //('multiple ( LCM ) of a series of numbers11()will give you an op)}portunity to use the 00((ideas of prime factorization and will 00((lead into ideas needed in future work 00(*}(on fractions. (OH goodie!!). 00((We'll look at several ways to view the //('idea of a least common multi+}lple in (subsequent pages. ( SECOND PAGE//('Let's consider finding the least common00((multipl,}e of 3 and 5. If we multiply //('these numbers by natural numbers,we get//('multiples of these numbers-for exampl-}e:" AA'3(3((Notice that some answers in the two ,(columns are the same!^ `&6-F:@,&-.}@@bK-@%(3&)-@%0(=>-@%K(@$dN-@"%(5&)-@'/}%0(=>-@)%J(@$N e$h PAGE 3m AAo6-F:@,r9-@%@(2-0}@)%@9(u-@w00((Note that I've highlighted the first |00((occurance of a duplication in 1}the two 00((lists. This number represents the LCM //('of 3 and 5. In theory, similar lists 00((can be made,2} and find the first dupli- 00((cation to find the LCM of several nos.   PAGE 46-@6-@  3}00((In practice, the preceeding techinique 00((is impractical to use. So let's view 11()the LCM in another w4}ay. 00((To view the idea in another way, note 00((that if a number is a multiple of 3 //('5}then it is divisible by 3. If a num- //('ber is a multiple of 5, then it is di- 11()divisible by 5. Thus the LCM i6}s the //('smallest number divisible by both 3 and//('5. Note that meets that criteria. & ( 0 PAGE 7}5://('Thus the LCM of 6 and 4 is , since ?00((12 is the smallest number divisible by D( both 6 and 4.((I8} AD@N*#(What is the LCM of 8 and 6'*(SC 4249((GOOD--you are absolutely correct. C ADEX//9}('NO, I'm sorry, but 24 is the LCM. ].('(What is the LCM of 5 and 15+.(_ ADUb: 4150(VERY GO:}OD--you've got the idea!: AD`g00((The LCM is 15. Both 5 and 15 divide i(evenly into 15. (  PAGE;} 6//('One more-what's the LCM of 162 and 135?//('(Just press if you have no idea) AD@(<}a48100;((You must know too much--I think you W(know what's coming up!!a AE \/('The LCM is 8100--don=}'t feel bad, I gave\((a hard one--we need a better way!!  B2(2('Fortunately there is a way to syste- >} 11()matically find the LCM of numbers. The //('technique depends on finding the prime 00((factorization of th?}e numbers involved. //('(I bet you knew we had to sneak that in( someplace!) (  PAGE 76-@ @}6- //('Let's consider a smaller example. Find00((the LCM of 50 and 15. A little thought  //('convincA}es you that the LCM is 150. 00(((150 = 3&50 and 150 = 10&15) ( 2 00((Note thB}at 50 = 2&5 15 = 3&5  //('To make the LCM just choose the largest%//('exponent of each disticnt factor and C} *00((write out the number using those expo- /00((nents. (of course no exponent means 1 400((is the exponent forD} that factor.) R ( \ PAGE 8a%%( 1f00(( 50 = 2 &5 15 = 3 &5 E} k//('Note that I've highlighted the largest p00((exponent for each distint factor. t( F} u//(' The LCM = 2 &3 &5 = 150 00((Now let's see if we can get the LCM of //('162 and 135. We firG}st find the prime //('factorizations and note the largest ++(# 4 3,,($exponentH}s: 162 = 2&3 135 = 5&3 ( 4//('LCM = 2&3 &5 = 8100 We noted that //('4 is the largest exponenI}t of the 3.   PAGE 900((To be sure you've got the idea lets 11()find the LCM of 45,78,28. Factor tJ}hem: ((( 2 200(( 45 = 3 &5 78 = 2&3&13 28 = 2 &7 00((Press when readyK} to continue.  AH0)@ B//('Now note the largest exponents: **(" L}1 1 00((45=3 &5 78=2 &3 &13 28=2 &7 ( 2 200((The LCM = 2 &3 &5&7&13 = 1M}6380 WOW !! //('This program will now give you the //('opportunity to practice finding the LCM//('of two nuN}mbers picked at random  $$: ( pCOVERPAGEzI+@%@/0@@@ I0@O}@@  l-@@+-@@P/ =6-@&IAUU-@h(@L cP} l $&##FLIPPAGE--A PSUEDO SUBROUTINE&( &( TO CONT.&(( TO BACKUPQ}&)@&;"AU6-%A+(>:A%,76-; &>"@f*( 6-&A.(>:A%,:6R}-> &"@'%D:MENU.*& A &"0@0@"$'!!CHLOAD-CHARACTER SET LOADER'E$S}6-+F:A,&@,$AVEPOKE 756,CHSET/256 TO ACTIVATE'2 AF:A,&@2AA$' #B%T}$'%-A6AU"!% )'PP104,162,4,160,0,177,205,145,203,200,208,249,230,206,230,204,202,208,242,96.'6U}-?:A6,3'j-@-%@H%1 M%@H%@@$jREPLACE & WITH A MULT. DOT8'$V}$,PPCHANGE DISPLAY LIST TO BE 10-GR1,1-GR2,2-GR1,1-GR2,2-GR1,1-GR2,2-GR1,1-GR2.,7+@%@76-F:A`,%F:AaW},$AV3, 8,S%@@+%@@?%@!@S%@$@B,0-@%@',X}%F:%@%,0 L,$,**PRTNO PRINT OUT EXPONENT IN COLOR, 6.=:,--@B:, - @>:@:7<Y},,%,- -$P-PRINT OUT FACTORS AND LCMZ-E-@@"(@4-@@E(@= d-Z}-n-1-F:@,@1(@8<,x-H8<@,!@/-F:@,@ H(@8<[}@,}-. -F:@,@.(@&- -E-@@"(@4-@@E(@\}= ---1-F:@,@1(@8<,-H8<@,!@/-F:@,@H(@]}8<@,-. -F:@,@.(@&- -*-@@*(@--^}-""8<,"@BP-?-F:@,@)6-8<,56-A(? 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IF YOUR ANSWER ISX*("CORRECT A MISSILE WILL FIRE AT THE-(X(&NUMBERS AND THEY WILL EXPLODE. IF Y%}OURZ.(&ANSWER IS WRONG NOTHING WILL HAPPEN.IFW($THE NUMBERS HIT THE GROUND THEY WILLZ(Y.(&EXPLODE AND YOU WILL LOS%}E A LIFE.AFTERY(&AN EXPLOSION THE SCORE WILL BE UPDATED##@@K: AW(SKILL LEVEL %}(1 TO 10)"GP:,) @)!@AWS=SKILL LEVEL BSET UP VARIABLES+@%@#%}6-$@/6-;6-@G6-S6-_6-@I1 AND I2 = KEYBOARD INPUT. Y=SCREEN ROWb6-P:%}$H:,,36-@%P:$H:,,?6-@bGENERATE TWO NUMBERS FOR PROBLEMMAIN LOOPy-%}+(@score =-@S(@lives g-@yI=SCREEN COLUMN -(@+%}%2@@@@G2@@@@U-@PY {2%}2@c"!-@@@(@ = J AcERASE ANSWER A%}T BOTTOM_-@@3(@ = _PRINT KEYBOARD ANSWER AT BOTTOM OF SCREEN"LOOK AT KEYBOARD%}, F:Ad,"AUA66-)@@"AUA`J'"6-&@H' AT%}!@A^'6-&@H%+$@,' Ah%Ar MISSILE|"-@%@6@%}0-%@?(@K6-@q2@u&@$@2@@x&@$@$?p%}R-@@ )-%@8(@ < H6-R AP6-\ -(@ %} .6-%@B"@AP\ERASE PROBLEM THEN STEP4 -@6@4AP86-%}%@%@A@8END OF MAIN LOOP!!EXPLOSIONS IN INVERSE VIDIOg!@#-&@@ 6(@%}ܡJ-&@@](@g AW"@-@ .(@ܡ:-@M(@%}W A44EXPLOSION SOUND FROM OCT/NOV '82 PAGE 11^-&@$(@ܡ*-=(@%}K-%@^(@44EXPLOSION SOUND FROM OCT/NOV '82 PAGE 11U%2@@u@@%}16-?=6-@I6-@U6-@2@ @;2@@@@W2@@%}p@_6-$q6-$+%?,6-$+%?,!@A}%2G2@%}i2@} @APERASE EXPLOSIONu@#-&@%}@ 8(@ L-&@@a(@ u"@A`z-@@0(@%}+=%D-AH Z-@@p(@ z A`&^-&@$(@ %}*-=(@ K-%@^(@ 0"@6-&@)6-@5"G-@@%}^(@ Šr-Av  A:)6-%@&6-@) A D7 +((#(%} AGAIN(Y/N)'74YAN)@(}(BASIC&(IS) D1:MATHWARS$]""MAMNNARRAPICLDRRCCHFLASCHBAECOCOVEINSTPAUSMOVCHROMUSIINKELEVOSETUPYZROUTCOCOATB)}ATUTPEMASTERTGOFDIPFALNNNZROUPOSNHRLYZL)} @)}@ !"#$)}%&'()*+,-./01234)}56789:;<=>?@ABC)}DEFGHii 1981 MULT 1-6 Macomb Inte)}rmediate School District ii by Kevin Collins )} 6-@6-?'6-@36-@?6-@K6-B@W6-BEc6-BP)}o6-@{6-B06-Bp6-Ao6-B6-B'6-B36-B?6-BK6-B )}W6-B%c6-B5o6-B0##@@K:SS9<,;A`,;@P,;A,9,;)}@,;@,;@,(. 6--@&68,-* . d -68,-n_16.'LET'S LOOK AT )}SOME EXAMPLES FROM LEVEL C67@@,.=:,G _6-@$+!@,x& &6-++'@,"P:'@,,}6.WATCH )}CAREFULLY - 6-6-!6-@-6-@. 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TO CONTINUE!6-A5p% 16-=6-@A EI #$'e6. ttttttttt6-@+6-@9-)}@I6-%$@S BW b6-$(+,e$t'6.7<, $)Y 6-6-@!6-@)-26.=:,6)} D6-%@H L Y(B) B B)H 6-6-A$-&6.=:,* 86-%A < @ )}E(H$) B B0* B *$*P 6.=:,6-@.6-A4%A $2 6 B6-L B)}P *8 6.X!6-A0%A$-6-@1 5 8$\+#,$@%@@5/A1@G/A1)}@Y,A6@k/A1@}/A&@ $,F 6.=:,6-(6-A4%A$, 0 <6-)}F B,S6-@%6-A0%$A)86.@6.I6-C:,S B0-6.mmmm B0 - )} 6-Bp$P-;6-+$@%@,$+!@,%@h$+ @,?[,@$@%@ g/@s)}/A1/A1@A,A&@FZ-./A1@A'/A6@F+ .$.?6-@6.=:$,#B:,)}"267@,.?67<,. ".#6-AR  #6-|.s-,$@%@$$@%@ C/$@%@)}$O/A(a/A(@Us,A#@`../A(@U'/A3@`+ .$.N 6-6-A&)}-)6-@96. tttttttttJ6.7@<,N .C6-%$@6.=:$,'B:,"667@,.C67<,. .%)} !6-%$@&$@% .26-@6-@% B/ B2$2? 6.-@'6. 56)}.7:,$W( (B%X   $Y+Y%%6-F:A`,%F:A*}a,$AVY))6-F:%@,%F:%@,$AVY--6-@%F:AA,%F:AB,$AVZ6-&@$+!@*}, Zoo6-+")"@)"@)"@,$@ %+")!@,$@@%+"@)"@,$@Z$[m*}6-@# 6-@(6-B:,.6-:6-@F6-m6-P:+@&+'@,,'@,&[067%<%,. *}  @&6-0 B5@[7%<%,4 B5@[ 6-& B5 [K6.7<%,6-%!6-B:,.7<,4 ;*}6.7<&,C6-&K6-%[J#6-+%&,$A%+@"&,' /6-%7%C6-@G J$\!6-@%!*}!6-&%\ B5 ]/ --$68<,-( , /$_@6-P:H:,$,%/6-P:H:,$,%@8<,*}BE_,68<,-6-%6-%)6.=:$,,$a $@%BP bgd6.ZhhhhhhhϠЅѥШ 4ΥѨ* }Ѩѥiԩ`ԅ`g$b>;6.1hhh`թשȭ@ȥ`>$ bkk6.a* }hhhhhhhhhhhhh******hheeiiЅ!btt67@,.a* }&e҅eӅٱJJJJԥ)eiЖ))"btq67A,.^ԥ))ԥ* }))ԥ))Нп٥ԑ ٥ՅȘ`t$Hq=6- AR+6-@=* }ARq#-@%@# \q8-@8(# 1981 Macomb Intermediate SchoolsfqO 6-6.MUL*}T06-@%P:@'B:,,4 =6.1-O67@,.=:,pq#6-Aa%P:@'B:,,# uq>-@@>(#Pres*}s 'S' to stop during the lessonzqzAdAU'-@@S(Which level to begin at (-)?Z)h6*}-&@Hz )!BPq (>:%@H,6-  $ D1:MULTIPLY(Q33ANSWEREB19NDISCUSSIOFLIPPAGCHARLOAUSERFACTOENTRFACTOGR1INPUFINDFACTOPRTNRANDOMPICCHGDISPLAYLISPR.}FACTOCOVERPAGDONFLAECHSECPAGPAGEONYENFMDEXPONENIBREA@.} .} !"#$%.}55PROGRAMMED BY BRIAN HOGAN AUBURN WA **** PFACTOR ****55PROGRAM FINDS PRIME FACTORIZATION OF A .}NUMBER N99;@,9@<@,;@,;@ ,(6. 236-A@6-A'6.}-B36-AP<?6-B6-A0'6-A36-A?6-BF36-A 6-B'6-B36.}-A`P6-B Z d LOAD ALT. CHAR SETf.@.@@K:n x  .} %D:MENU.*FACTOR A NUMBER ND-@+-@<68<,-@ D 6-.}%6-@ A%Ap%6-@ A%Ap'6-%@ A'Ap$ .}AP.$8FILL UP THE E(I,J) MATRIXB6-LB $!68<,-368<@,-@?6-@B$.}VP:','AP`868<,-868<@,-8<@,%@j 6-'t A~(8<@,.}(6-%@$xGR1INPUT6-6-)@"AU$!!"@H*".}A --+ @H)!@W,*"A "A&*6@F:@,&@F(@ c.}@F:@,&@t6-P:'@,6-&@ A a!@G* @X'6-%@A6-@$%+&. }@H,W(@&@Ha A A !C!-@.(@@-@@b(@.!}>:A8,>:AW,l A9 DIGIT ACCURACY A -+@%@ -AV'AV 6."}-AP0-@@0(@ try to factor6-P:$H:@,,%@"-@@"(@.#}4-@@4(@ for answer  )@ AUA p* 45-@@5.$}(@ for another>,-@@ ,(@ to stopH)@R"@$\AU.%}A! f-(@p$-&@$(@z"-@"(@"-@.&}"(@"-@ "(@ A 0 ##FACTOR a number given by user   AV'AV.'} 2-@@2(@enter number to .-@@.(@ be factored ;-@@7(@.(}>:A8,>:AW,;  D"@6-@'-@:(@@D A0     2-@.)}@2(@ TO CONT. 0-@@0(@ OR TO STOP& )@0 "@$: .*}AUA0D "-@"(@N -(@X $-&@$(@b /-.+}@"(@/(@l A0P!!DISCUSSION OF PRIME NUMBERS6-A@6-@ +.,}'0@A0@@@[0@@@m@@SETCOLORS AND LEFT MARGIN.-} )()( P R I M E N U M B E R S %%(  ( (5(5(* The PRIME NUMBERS ..}have long held a 00((particular fascination to mathemat- 11()icians of the present and past. The 11(./})primes have long been recognized as the //('building blocks of the natural numbers. ( DEFINITION: 00(( .0} A PRIME number is a natural number ,,($that has exactly 2 natural number ( ( divisors..1}(( EXAMPLES:11()7 is a prime since only 1 and 7 divide "--(%evenly into 7. 10 is not a prime $!!( .2} '22(*since it has 4 divisors--1,2,5 and 10. ,00((1 is NOT a prime either. It only has 1(.3}1 divisor--namely 1.(6 ^70@@@70@@@h(A LITTLE TEST:(m&&((A) I.4}s 23 a prime number(Y,N)o   (r( Correct!! AB w--(%Wrong, 23 only has 2 divisors(23, 1).|)()((B).5} Is 77 a prime number(Y,N)~   (,"(Correct--good for you., AB@--(%I'm sorry, you are incorrect. 77 ha.6}s!!(4 divisors--1, 7, 11, 77.)()((C) Is 31 a prime number(Y,N)   ( ( RIGHT ON!! AB`,,($.7}Your number facts are a little mixed//('up perhaps. 31 has 2 divsors(1,31). ,(,( (D) Is 91235 a prime number(Y,N.8})   (\2(&WRONG, you forgot that a number endingR(in a 5 is divisible by 5. \ ABG.(&RIGHT!--You m.9}ust have noticed that theG(number ended in a 5. ( 70@@@70@@@( DE.:}FINITION:(55(-If a number, greater than one, is not a 11()prime, than it is a COMPOSITE number. 5(5(*.;}It turns out that any composite number 22(*can always be written as a unique 11()product of primes( ignori.<}ng order). &(&(EXAMPLE: 24=2 x 2 x 2 x 3( 45=3 x 3 x 54(4()We'll get into this in a minu.=}te or so.   05(5(*In general it can be very difficult to 500((find the prime factors of a number, :11.>}()especially when it is a large number!! D11()In theory it's very simple--just start I11()dividing by the natural .?}numbers to see N11()if there are any divisors( other than 1 S11()and the original number ). Just try X00((a .@}'small' number like 70,000,000,001! b ( 11()For large numbers, the computer is used 11()to do this time cons.A}uming task. How- 11()ever it is not inconceivable that it 11()could take even the fastest computer ,,(.B}$CENTURIES to factor large numbers!! ( 11()Obviously this li'l ol' ATARI ain't in 00((the BIG leagu.C}es, so we'll stick to !!(smaller values to factor.3(3((First we'll let you pick some numbers 00((to be .D}factored, then the computer will ..(&pick some at random for YOU to factor. ( 70@@@70@.E}@@!!( FACTORING NUMBERS!!(  6( (6((You will be asked to ente.F}r some number 00((that you want to see factored. Due to //('the limitations of the computer, keep 11()the num.G}ber you enter less than  00(( 99,999,999 (an itty-bitty no.!!) %4(4()The factored number will be show.H}n to **'(you in a form using exponents. *(H \00((The factored number is found by a00((dividing by.I} first 2, then the odd f00((numbers up until you get to the square k11()root of the number you're factoring. .J} p//('Sometimes it may take 20-30 seconds u00((to factor a larger number--be patient  $??USER FACTO.K}RS THE NUMBERS AND CHECKS ANSWER WITH COMPUTER.6-AP6-@m +'0@A0@.L}@@ [0@@@ m@@AV'AV //('NOW, you can practice fact.M}oring some //('numbers into it's prime factors. ++(#Believe it or not, you do have some!!( .N} //('advantage over a dumb computer. You //('have the advantage of seeing the over- ( all number. .O} 7( (7()If a number ends in a 5, for example, 00((then you can skip trying to factor it 11()using a 2 and.P} immediately use a 5 //('instead. EXAMPLE: 335 = 5 x 67 11()(The 67 comes by dividing 5 into 335) .Q} //('There are other shortcuts that you may //('have learned in your past work in math.00((A number ending i.R}n 0 is divisible by 00((10. A number ending in 00 is diviible 00((by 100....etc. The 10 (or 100) is //(.S}'then easily broken up. Then you can  //('concentrate on the remaining factor. //('EXAMPLE: 600 = 6 x 100 = 2&3.T}&2&5&2&5 //('EXAMPLE: 350 = 35 x 10 = 5&7&2&5 II(AIf you use exponents, then the above 3.U} 255(-answers look like 2 &3&5 and 2#( 2&5 &7.  P00((I'm sure that you know that an even .V} U//('number always has 2 as a factor and Z00((is recognizable by the fact that the _//('last digit is divi.W}sible by 2. Did you d//('know that a number is divisible by 4 i00((if the last 2 digits(as a number) is n00((d.X}ivisible by 4? EXAMPLE: 524 = 4&131 s//('( The 24 at the end was the clue!!) x00((EXAMPLE: 3744904 is divisible .Y}by 4. }00((EXAMPLE: 36400 = 100&364 = 100&4&91 = ""( 2&5&2&5&2&2&91 =( 4 2( .Z} 2 &5 &91 //('There are neat ways to test divisibil- 00((ity by 3 and 9. If the of the //('.[}digits is divisible by 3 (or 9) then //('the number itself is divisible by 3 00(((or 9). EXAMPLE: 351 = 9&39 .\}since ""(3+5+1=9 is divisible by 9.2(2('EXAMPLE: 5463 is divisible by 9 since00((5+4+6+3=18 is divisible.]} by 9 (9&607) 00((EXAMPLE: 5445 = 5&1089 (ends in a 5) 00(( = 5&9&121 (1+0+8+9=18) ##( .^} = 5&3&3&11&11 ( 00((EXAMPLE: 57 is divisible by 3 since 00((the sum of the digits is divisible by._} "$$(3. (5+7=12) Thus 57 = 3&19,(600((Unfortunately, not all numbers are as ;//('easy to crack. There is.`} no easy test @00((for every kind of factor. It some- J00((times breaks down to just trying dif- O00((ferent.a} factors. Try 7, try 13, try 17 T00((etc. etc.&&&&&&. Fortunately, most Y00((problems in math texts have been ch.b}os- ^//('en to be cracked easily. However in c++(#real life, things can be tougher!! h |(IT'S YOUR TURN!.c}( 00((The computer will pick some numbers at 00((random for YOU to factor. Try some of 00(.d}(the hints given you in the previous 00((discussion. Also remember, there might 00((be some PRIME numbers picked.e} and hence 22(*there are no factors to find. 00((When you're ready to check your answer 00((just pr.f}ess to see the computers "(answer. 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H(@2} DIVISORS:&@a(@ GUESSES:&'6-@6-@'6-@ &9%2@P@@92}-@@'C-@@0?0@P:H:,$@,@C ') )22}'$',THESE GAMES WILL'TEST YOUR KNOWLEDGE$'OF DIVISION..',THE COMPUTER WILL8'RANDOMLY CHOOSE ANB'2}INTEGER THAT YOUL'WILL TRY TO DEDUCE.V',GIVE THE COMPUTER`'A NUMBER TO DIVIDEj'INTO THE HIDDEN ONEt'AND2} IT WILL RETURN~'SOME INFORMATION TO'YOU CONCERNING THE'THE REMAINDER.',THE EXACT RESPONSE'FROM THE C2}OMPUTER'DEPENDS ON WHICH'GAME YOU ARE PLAY-'ING. IN THE HARDER'GAMES YOU GET LESS'INFORMATION.'2},IN GAME 1 YOU ARE'TOLD THE REMAINDER.',IN GAME 2 YOU KNOW(WHETHER THE REM. IS (ODD OR EVEN. (ALSO(TH2}ERE IS NO PRIME(FACTOR > 31.)((,IN GAME 3 YOU ARE2(TOLD ONLY WHETHER<(THE REMAINDER IS 0F(OR NOT. (BUT T2}HEP(RANGE OF POSSIBLEZ(VALUES IS REDUCED).d(,GAME 4 IS SIMILARn(TO GAME 3 EXCEPTx(THAT THE RANGE OF(2}VALUES HAS BEEN(INCREASED.(,IN HOW FEW GUESSES(CAN YOU DEDUCE THE(HIDDEN NUMBER ?? D1:REMGAME0ySEATTLE-PUGET SOUND ATARI COMPUTERENTHUS- IASTS Disk #33Mathe- maticsUpdated:Jan11,87Librarian - Jim Chapman