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 AZ
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 20070916 11:43:34 