All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Grid and Equal Subgrids (Posted on 2009-08-14)
Substitute each of the capital letters in bold in this 3x3 grid by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subgrids is equal to 9*E.

A   B   C
D   E   F
G   H   I

What will be the arrangement(s) (disregarding reflections and rotations), if keeping all the other conditions unchanged, the sum of digits in each of the four 2x2 subgrids is equal to 7*E?

 See The Solution Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 3 of 4 |

To avoid reflections/rotations, A is the lowest corner and C is less than G:

CLS
FOR a = 1 TO 6
used(a) = 1
FOR c = a + 1 TO 8
used(c) = 1
FOR g = c + 1 TO 9
used(g) = 1
FOR i = 1 TO 9
IF used(i) = 0 THEN
used(i) = 1

FOR b = 1 TO 9
IF used(b) = 0 THEN
used(b) = 1
FOR d = 1 TO 9
IF used(d) = 0 THEN
used(d) = 1
FOR f = 1 TO 9
IF used(f) = 0 THEN
used(f) = 1
FOR h = 1 TO 9
IF used(h) = 0 THEN
used(h) = 1
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
IF a + b + d + e = 9 * e OR a + b + d + e = 7 * e THEN
PRINT
PRINT a; b; c
PRINT d; e; f
PRINT g; h; i
PRINT (a + b + d + e) / e
END IF
END IF
END IF
END IF
END IF
used(h) = 0
END IF
NEXT
used(f) = 0
END IF
NEXT
used(d) = 0
END IF
NEXT
used(b) = 0
END IF
NEXT b

used(i) = 0
END IF
NEXT i
used(g) = 0
NEXT g
used(c) = 0
NEXT c
used(a) = 0
NEXT a

produces

` 1  9  2 8  3  7 4  6  5 7`
` 3  4  5 9  2  7 6  1  8 9`
` 4  3  5 9  2  8 6  1  7 9`

In each case, the multiple appears below the array.

 Posted by Charlie on 2009-08-14 15:34:21

 Search: Search body:
Forums (0)