* FROM PD DISK UNF # 3 .{ GRAPHICS,ENHANCEMENTS AND INSTRUCTIONS BY JIM GREEN .53280,5:53281,12:(142);" ";"ѣѷѷѣ ѷѣѷѣ ѣ ѷ* " W " " ў  "ў  " ў ў   " ѠB " Ѡ Ѡ p " "  "" ў ў ў ў ў  &"ў ў ў  6 '" d (" )" *" +" ";# ," T H E M A T H E M A T I C A L ";T -" "; ." W O N D E R O F T H E "; /" "; 0" T W E N T I E T H C E N T U R Y "; 1" ". 2D14400::""D 453280,7:53281,7t 6" RESS <> FOR INSTRUCTIONS 8" RESS <> TO PLAY AILSTONES <J$:J$"I"J$"H"60 @J$"H"200 d53280,12:53281,12:" HERE IS A SIMPLE BUT NEVERTHELESS6f" EXTREMELY INTERESTING PROBLEM OFah" MATHEMATICS WHICH MAY BE STATED ASj" FOLLOWS. IVEN ANY POSITIVE NUMBERl" LET'S CALL IT '', TREAT '' IN THEn" IN THE FOLLOWING MANNER - F '' IS p" ODD, MULTIPLY IT BY 3 AND ADD 1.2r" N ASIC IT MAY BE WRITTEN -_t" =*3+1, IF NEW RESULTS IS EVEN THENv" DIVIDE BY 2 - ASIC =/2 -x" HE QUESTION. HEN '' IS TREATEDz" THIS WAY WHAT HAPPENS TO '' ? ?|" RESS <> TO CONTINUE~198,0:198,1A" F WE TAKE THE NUMBER 7 YOU WILL FINDn" THAT IT EVENTUALLY REACHES THE NO. 1" BECAUSE 7 IS ODD, AND MULTIPLYING" 7 BY 3 AND ADDING 1, (=*3+1), " BECOMES 22. INCE 22 IS EVEN,IT IS" DIVIDED BY 2, (=/2), TO YIELD 11,F" NOW 11 BEING ODD, IS MULTIPLIED BY 3t" WITH 1 ADDED, GIVING 34. HIS IN TURN" BECOMES 17,52,26,13,40,20,10,5,16,8" 4,2, AND FINALLY 1." RESS <> TO CONTINUE198,0:198,1$" T HAS BEEN SAID THAT ALL POSITIVEQ" NUMBERS WHEN TREATED IN THIS FASHIONs" EVENTUALLY CONVERGE TO 1." HE FACT IS THAT NOBODY IN THE WORLD" HAS YET PROVED THAT THIS IS THE CASE," NOR HAS IT BEEN DISPROVED.LL WE CAN%" BE SURE OF IS THAT NO ONE HAS YETS" FOUND A NUMBER THAT DOES NOT CONVERGEa" TO 1." RESS <> TO CONTINUE198,0:198,1" AKE YOUR TRUSTY OLD -64 OMPUTER AND" TRY TO FIND A NUMBER THAT DOSN'T GO&" TO 1, IF YOU ARE SUCESSFUL,YOU WILLN" BECOME AND PERHAPSy" RICH. HEN YOU COLLECT YOUR PRIZE," DON'T FORGET TO THANK YOUR OLD" FAITHFUL -64 . Ġˠ!!" HE NUMBER 27 IS A GOOD ONE TO TRY.#" RESS <> TO CONTINUE5198,0:198,1] HAILSTONES ZAPPERS FOR C64 P37 .53280,5:53281,12:54296,15:(142):"";T15:"";:" H A I L S T O N E S ";T15:"";::""'" PICK A NUMBER, ANY NUMBER";N;N(N)N0245k" NO NOT THAT NUMBER!":D1600::225}QN:IT0:""Q1295ITIT1:EVEN(Q2(Q2))EVEN275 QQ31280QQ2" OPERATION #"IT;26)Q340"250'" YES,"N;:,"GOES TO 1 IN"IT"OPERATIONS!C1370`6" ANOTHER (Y/N)? ";};A$:A$"Y"A$"N"315@A$:D1500:EA$"Y"205J"FINISHEDOT SOUNDYFR17167:EVEN FR8291^54272,FR 255c54273,(FR256))h54277,34:54278,34:54276,17ZmI1200::54276,16:T5427254295:T,0::hr SUCCESSywHI16:LO195|54277,34:54278,34:54277,LO:54273,HI:54276,17I116:54276,16:54276,17:LOLO9LO256400LOLO256:HIHI1:39054272,LO:54273,HI:I54276,16:I1200::54272,15:54273,6754276,17:I120::54276,16:T5427254295:T,0: