Solve this alphametic, where each of the small letters in bold represents a different decimal digit from 0 to 9. None of the numbers can contain any leading zero.

(five)² = (four)² + (tri)²

(In reply to Alphametric computer soltuion by Brian Smith)

Indeed:

DEFDBL A-Z
FOR f = 1 TO 9
 used(f) = 1
FOR t = 1 TO 9
IF used(t) = 0 THEN
 used(t) = 1
FOR i = 0 TO 9
IF used(i) = 0 THEN
 used(i) = 1
FOR v = 0 TO 9
IF used(v) = 0 THEN
 used(v) = 1
FOR e = 0 TO 9
IF used(e) = 0 THEN
 used(e) = 1
 five = f * 1000 + i * 100 + v * 10 + e
FOR o = 0 TO 9
IF used(o) = 0 THEN
 used(o) = 1
FOR u = 0 TO 9
IF used(u) = 0 THEN
 used(u) = 1
FOR r = 0 TO 9
IF used(r) = 0 THEN
 used(r) = 1
 four = f * 1000 + o * 100 + u * 10 + r
 tri = t * 100 + r * 10 + i
 IF five * five = four * four + tri * tri THEN
   PRINT five; four; tri
 END IF
 used(r) = 0
END IF
NEXT
 used(u) = 0
END IF
NEXT
 used(o) = 0
END IF
NEXT
 used(e) = 0
END IF
NEXT
 used(v) = 0
END IF
NEXT
 used(i) = 0
END IF
NEXT
 used(t) = 0
END IF
NEXT
 used(f) = 0
NEXT

produces

 1496  1320  704

only.

Posted by Charlie on 2009-04-18 17:27:21