I chose a certain sequencing rule, and I told my friend no matter what number he named, it would eventually end up at repeating 4s.

At first he chose 5, which ended in 4, 4, 4... Then he tried 18, which met the same fate. Even numbers like -42 and Pi ended in 4, 4, 4...

Still trying to outdo me, he started to get really creative. He tried 63424563562324 ... same. He even tried a googolplex and Avogadro's number. But alas all the numbers he tried ended up in 4,4,4. Finally he conceded.

What's the sequencing rule I use? Should he have conceded? Can you find any starting terms which don't end in 4, 4, 4...?

sixty-three trillion four hundred twenty-four billion five hundred sixty-three million five hundred sixty-two thousand three hundred twenty-four                          123
one hundred twenty-three     21
twenty-one     9
nine           4
four           4
four           4
four           4
four           4
four           4
four           4
four           4

DEFDBL A-Z
DECLARE SUB ProcPiece (piece$, MajorPower)
DATA one,two,three,four,five,six,seven,eight,nine
DATA ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen
DATA eighteen,nineteen
DATA twenty,thirty,forty,fifty,sixty,seventy,eighty,ninety
DATA thousand,million,billion,trillion,quadrillion,quintillion,sextillion
DIM SHARED unit$(19), ten$(10), major$(7)
FOR i = 1 TO 19
  READ unit$(i)
NEXT
FOR i = 2 TO 9
  READ ten$(i)
NEXT
FOR i = 1 TO 7
  READ major$(i)
NEXT
DIM SHARED name$, num$
n = 63424563562324#
FOR iterations = 1 TO 33
        num$ = LTRIM$(STR$(n))
        IF num$ = "0" THEN
                name$ = "zero"
        ELSE
                name$ = ""
                MajorPower = 0
                DO
                        l = LEN(num$): IF l > 3 THEN l = 3
                        piece$ = RIGHT$(num$, l)
                        num$ = LEFT$(num$, LEN(num$) - l)
                        CALL ProcPiece(piece$, MajorPower)
                        MajorPower = MajorPower + 1
                LOOP WHILE LEN(num$) > 0
        END IF
        tVal = 0
        FOR i = 1 TO LEN(name$)
          lt$ = MID$(name$, i, 1)
          IF INSTR("abcdefghijklmnopqrstuvwxyz", lt$) > 0 THEN
            tVal = tVal + 1
          END IF
        NEXT
        n = tVal
        PRINT name$, n
'        IF tVal = 100 THEN PRINT n
NEXT

SUB ProcPiece (piece$, MajorPower)
  piece = VAL(piece$)
  n$ = ""
  IF piece > 99 THEN
    n$ = unit$(piece \ 100) + " hundred "
    piece = piece MOD 100
  END IF
  IF piece > 19 THEN
    n$ = n$ + ten$(piece \ 10)
    piece = piece MOD 10
    IF piece > 0 THEN n$ = n$ + "-":  ELSE n$ = n$ + " "
  END IF
  IF piece > 0 THEN n$ = n$ + unit$(piece) + " "
  IF n$ > "" THEN name$ = n$ + major$(MajorPower) + " " + name$
END SUB

Edited on August 7, 2007, 12:22 pm

Posted by Charlie on 2007-08-07 12:17:12