Substitute each of the small letters in bold by a different decimal digit from 0 to 9 to satisfy this alphametic equation:

(one)/(five) = .two

where, none of o, f and t is zero, and the 3-digit number represented by two is even.

Note: Try to derive a non computer-assisted solution, although computer program/spreadsheet solutions are welcome.

DECLARE SUB permute (a$)
CLS
a$ = "onefivtwxx": h$ = a$
DO
 o = INSTR(a$, "o") - 1
 f = INSTR(a$, "f") - 1
 t = INSTR(a$, "t") - 1
 IF o > 0 AND f > 0 AND t > 0 THEN
   i = INSTR(a$, "i") - 1
   v = INSTR(a$, "v") - 1
   w = INSTR(a$, "w") - 1
   n = INSTR(a$, "n") - 1
   e = INSTR(a$, "e") - 1
   two = t * 100 + w * 10 + o
   five = f * 1000 + i * 100 + v * 10 + e
   one = o * 100 + n * 10 + e
   IF two * five = one * 1000 THEN
     PRINT one; five; two
   END IF
 END IF
 permute a$
LOOP UNTIL a$ = h$

finds

one  five  two
528  1408  375
495  1875  264

but 375 is not even, so it's 495 / 1875 = .264

Posted by Charlie on 2008-11-24 18:33:35