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 Deduction Problem (Posted on 2014-01-31)
```     AZA
x AZZA
---------
AZZZZZA
```
Substitute a single digit for Z. Substitute any digit for each A. The number for Z must be different from the numbers for A. There are no leading zeros. What are the possible solutions?

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 computer solution Comment 1 of 1

DEFDBL A-Z
CLS
FOR z = 0 TO 9
FOR a1 = 1 TO 9
IF a1 <> 0 THEN
FOR a2 = 0 TO 9
IF a2 <> z THEN
m1 = 100 * a1 + 10 * z + a2
FOR a3 = 1 TO 9
IF a3 <> z THEN
FOR a4 = 0 TO 9
IF a4 <> z THEN
m2 = 1000 * a3 + 110 * z + a4
FOR a5 = 1 TO 9
IF a5 <> z THEN
FOR a6 = 0 TO 9
IF a6 <> z THEN
p = 1000000 * a5 + 111110 * z + a6
IF m1 * m2 = p THEN
PRINT m1: PRINT m2: PRINT p
END IF
END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT
NEXT

finds

723
7223
5222229

and

645
8441
5444445

 Posted by Charlie on 2014-01-31 22:00:07

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