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Making poverty history (Posted on 2006-02-19) Difficulty: 3 of 5
On New Years Day, Penny resolved to make poverty history.

Unfortunately Penny was penniless and asking her relatives for cash seemed a bit passe, so she asked them to contribute goats.

Frankie, Mark, Dolly, Squidly, Ruby and Draco each sent goat vouchers. Each of the vouchers was for a three figure number of goats. Penny was delighted with the response, over 5200 goats in total. Even better, she found that after using 11 of the goats to pay local administrative expenses, each of the beneficiaries would receive exactly 32 goats.

Curiously she noticed that the each of the donations was the product of exactly six prime numbers. If Frankie gave more than Mark, who gave more than Dolly, who gave more than Squidly, who gave more than Ruby, who gave more than Draco, how many did each give?

No Solution Yet Submitted by goFish    
Rating: 4.5000 (4 votes)

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Solution computer solution | Comment 1 of 9

This program finds all three-digit numbers that have exactly six prime factors:

DEFDBL A-Z

CLS

FOR nbr = 100 TO 999
  factor nbr, nfct$
  fct = 0: st = 1
  DO
    ix = INSTR(st, nfct$, " ")
    IF ix THEN fct = fct + 1
    st = ix + 1
  LOOP UNTIL ix = 0
  IF fct = 6 THEN PRINT nbr; ",";
NEXT


END

SUB factor (num, s$)
 s$ = "": n = ABS(num): IF n > 0 THEN limit = sqroot(n):  ELSE limit = 0
 IF limit <> INT(limit) THEN limit = INT(limit + 1)
 dv = 2: GOSUB DivideIt
 dv = 3: GOSUB DivideIt
 dv = 5: GOSUB DivideIt
 dv = 7
 DO UNTIL dv > limit
   GOSUB DivideIt: dv = dv + 4 '11
   GOSUB DivideIt: dv = dv + 2 '13
   GOSUB DivideIt: dv = dv + 4 '17
   GOSUB DivideIt: dv = dv + 2 '19
   GOSUB DivideIt: dv = dv + 4 '23
   GOSUB DivideIt: dv = dv + 6 '29
   GOSUB DivideIt: dv = dv + 2 '31
   GOSUB DivideIt: dv = dv + 6 '37
   IF INKEY$ = CHR$(27) THEN s$ = CHR$(27): EXIT SUB
 LOOP
 IF n > 1 THEN s$ = s$ + STR$(n)
 EXIT SUB

DivideIt:
 DO
  q = INT(n / dv)
  IF q * dv = n AND n > 0 THEN
    n = q: s$ = s$ + STR$(dv): IF n > 0 THEN limit = sqroot(n):  ELSE limit = 0
    IF limit <> INT(limit) THEN limit = INT(limit + 1)
   ELSE
    EXIT DO
  END IF
 LOOP
 RETURN
END SUB

Those numbers are used as data in the following program:

DATA 144 , 160 , 216 , 224 , 240 , 324 , 336 , 352 , 360 , 400 , 416 , 486 , 504
DATA 528 , 540 , 544 , 560 , 600 , 608 , 624 , 729 , 736 , 756 , 784 , 792 , 810
DATA 816 , 840 , 880 , 900 , 912 , 928 , 936 , 992
 
DIM n(34)
FOR i = 1 TO 34: READ n(i): PRINT n(i): NEXT

FOR draco = 1 TO 29
 t = n(draco)
 FOR ruby = draco + 1 TO 30
  t = t + n(ruby)
  FOR squidly = ruby + 1 TO 31
   t = t + n(squidly)
   FOR dolly = squidly + 1 TO 32
    t = t + n(dolly)
    FOR mark = dolly + 1 TO 33
     t = t + n(mark)
     FOR frankie = mark + 1 TO 34
      t = t + n(frankie)
      IF t MOD 32 = 11 AND t >= 5200 THEN
        PRINT n(draco); n(ruby); n(squidly); n(dolly); n(mark); n(frankie), t
      END IF
      t = t - n(frankie)
     NEXT frankie
     t = t - n(mark)
    NEXT mark
    t = t - n(dolly)
   NEXT dolly
   t = t - n(squidly)
  NEXT squidly
  t = t - n(ruby)
 NEXT ruby
NEXT draco

It reports, in order from least (draco) to greatest (frankie), and the total:

729  810  880  912  936  992              5259

  Posted by Charlie on 2006-02-19 12:31:52
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