Each of the capital letters in bold in this 3x3 grid is to be substituted by a different digit from 1 to 9 such that :

• Each of A, C, G and I is even, and:
• The sum of the digits in each of the four 2x2 subgrids is equal.

A   B   C
D   E   F
G   H   I

Disregarding the rotations and reflections, how many distinct solutions are there?

 2  5  4
 9  3  7
 6  1  8

 2  9  4
 3  7  1
 6  5  8

from

a = 2
FOR c = 4 TO 6 STEP 2
FOR g = c + 2 TO 8 STEP 2
i = 20 - a - c - g

FOR b = 1 TO 9 STEP 2
FOR d = 1 TO 9 STEP 2
IF d <> b THEN
  FOR f = 1 TO 9 STEP 2
   IF f <> d AND f <> b THEN
  FOR h = 1 TO 9 STEP 2
   IF h <> d AND h <> b AND h <> f THEN
    IF a + d = c + f THEN
    IF b + c = h + i THEN
    IF f + i = d + g THEN
    IF g + h = a + b THEN
       e = 45 - a - b - c - d - f - g - h - i
       PRINT
       PRINT a; b; c
       PRINT d; e; f
       PRINT g; h; i

    END IF
    END IF
    END IF
    END IF
   END IF
  NEXT
   END IF
  NEXT
END IF
NEXT
NEXT

NEXT
NEXT

Posted by Charlie on 2009-08-18 16:31:33