Each of the letters should be replaced by a different digit from 0 to 9 to satisfy this alphanumeric equation:

ALIGN = ANY * SET

Can you solve it, knowing that if I told you what E stood for, you would be able to tell me all the other letters?

(In reply to Answer by Joe)

A general rule is leading zeros are not allowed. If they were, a more complete list would be:

03792 = 024 * 158
04732 = 028 * 169
06794 = 043 * 158
08234 = 046 * 179
08463 = 039 * 217
09246 = 067 * 138
09486 = 062 * 153
29458 = 286 * 103
29870 = 206 * 145
31752 = 324 * 098
35476 = 362 * 098
36594 = 342 * 107
47586 = 462 * 103
57936 = 568 * 102
67392 = 624 * 108
86394 = 847 * 102

in which case 1, 6 and 7 would also be values of E that would produce unique assignments.  Zero is considered just as invalid for S as for A.

DEFDBL A-Z
CLS

FOR a = 0 TO 9
 taken(a) = 1
FOR l = 0 TO 9
 IF taken(l) = 0 THEN
  taken(l) = 1
 
FOR i = 0 TO 9
 IF taken(i) = 0 THEN
  taken(i) = 1

FOR g = 0 TO 9
 IF taken(g) = 0 THEN
  taken(g) = 1

FOR n = 0 TO 9
 IF taken(n) = 0 THEN
  taken(n) = 1

FOR y = 0 TO 9
 IF taken(y) = 0 THEN
  taken(y) = 1

FOR s = 0 TO 9
 IF taken(s) = 0 THEN
  taken(s) = 1

FOR e = 0 TO 9
 IF taken(e) = 0 THEN
  taken(e) = 1

FOR t = 0 TO 9
 IF taken(t) = 0 THEN
  taken(t) = 1

   anyV = a * 100 + n * 10 + y
   setV = s * 100 + e * 10 + t
   anyset = anyV * setV
   align = a * 10000 + l * 1000 + i * 100 + g * 10 + n
   IF anyset = align THEN
      al$ = RIGHT$("00000" + LTRIM$(STR$(align)), 5)
      an$ = RIGHT$("000" + LTRIM$(STR$(anyV)), 3)
      se$ = RIGHT$("000" + LTRIM$(STR$(setV)), 3)
      PRINT al$; " = "; an$; " * "; se$
   END IF

  taken(t) = 0
 END IF
NEXT

  taken(e) = 0
 END IF
NEXT

  taken(s) = 0
 END IF
NEXT

  taken(y) = 0
 END IF
NEXT

  taken(n) = 0
 END IF
NEXT

  taken(g) = 0
 END IF
NEXT

  taken(i) = 0
 END IF
NEXT
 
  taken(l) = 0
 END IF
NEXT
 taken(a) = 0
NEXT

 

Edited on September 16, 2007, 11:45 am

Posted by Charlie on 2007-09-16 11:43:34