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 Even Corners and Equal Subgrids (Posted on 2009-08-18)
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?

 See The Solution Submitted by K Sengupta No Rating

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 computer solution | Comment 3 of 5 |

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

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