## Squares, subsquares and arrangement puzzle

Substitute each of the capital letters in this 3x3 square by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subsquares is equal to 6*E.

A B C
D E F
G H I

What will be the arrangement(s), if keeping all the other conditions unaltered, the sum of digits in each of the four 2x2 subsquares is equal to 5*E?

Note: The rotations and reflections of a valid arrangement are considered as the same solution.
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 Blog Entries: 2 Part 1 of the puzzle: Spoiler There are 8 solutions, however solution 2-8 are either reflections or rotations of solution 1. solution1: a=4 b=2 c=7 d=9 e=3 f=6 g=5 h=1 i=8 solution2: a=4 b=9 c=5 d=2 e=3 f=1 g=7 h=6 i=8 solution3: a=5 b=1 c=8 d=9 e=3 f=6 g=4 h=2 i=7 solution4: a=5 b=9 c=4 d=1 e=3 f=2 g=8 h=6 i=7 solution5: a=7 b=2 c=4 d=6 e=3 f=9 g=8 h=1 i=5 solution6: a=7 b=6 c=8 d=2 e=3 f=1 g=4 h=9 i=5 solution7: a=8 b=1 c=5 d=6 e=3 f=9 g=7 h=2 i=4 solution8: a=8 b=6 c=7 d=1 e=3 f=2 g=5 h=9 i=4 solution1: a=4 b=2 c=7 d=9 e=3 f=6 g=5 h=1 i=8 4 2 7 9 3 6 5 1 8 solution2: a=4 b=9 c=5 d=2 e=3 f=1 g=7 h=6 i=8 4 9 5 2 3 1 7 6 8 (reflection of solution 1 along the AI-line) solution3: a=5 b=1 c=8 d=9 e=3 f=6 g=4 h=2 i=7 5 1 8 9 3 6 4 2 7 (reflection of solution 1 along the DF-line) solution4: a=5 b=9 c=4 d=1 e=3 f=2 g=8 h=6 i=7 5 9 4 1 3 2 8 6 7 (rotation of solution 1 by 90° to the right) solution5: a=7 b=2 c=4 d=6 e=3 f=9 g=8 h=1 i=5 7 2 4 6 3 9 8 1 5 (reflection of solution 1 along the BH-line) solution6: a=7 b=6 c=8 d=2 e=3 f=1 g=4 h=9 i=5 7 6 8 2 3 1 4 9 5 (rotation of solution 1 by 90° to the left) solution7: a=8 b=1 c=5 d=6 e=3 f=9 g=7 h=2 i=4 8 1 5 6 3 9 7 2 4 (rotation of solution 1 by 180°) solution8: a=8 b=6 c=7 d=1 e=3 f=2 g=5 h=9 i=4 8 6 7 1 3 2 5 9 4 (reflection of solution 1 along the CG-line)
 Blog Entries: 2 Part 2 of the puzzle: Spoiler Part 2 of puzzle: With the 5*E condition we get 16 solutions: solution1: a=1 b=6 c=7 d=9 e=4 f=3 g=2 h=5 i=8 solution2: a=1 b=9 c=2 d=6 e=4 f=5 g=7 h=3 i=8 solution3: a=2 b=5 c=3 d=9 e=4 f=8 g=6 h=1 i=7 solution4: a=2 b=5 c=8 d=9 e=4 f=3 g=1 h=6 i=7 solution5: a=2 b=9 c=1 d=5 e=4 f=6 g=8 h=3 i=7 solution6: a=2 b=9 c=6 d=5 e=4 f=1 g=3 h=8 i=7 solution7: a=3 b=5 c=2 d=8 e=4 f=9 g=7 h=1 i=6 solution8: a=3 b=8 c=7 d=5 e=4 f=1 g=2 h=9 i=6 solution9: a=6 b=1 c=7 d=9 e=4 f=8 g=2 h=5 i=3 solution10: a=6 b=9 c=2 d=1 e=4 f=5 g=7 h=8 i=3 solution11: a=7 b=1 c=6 d=8 e=4 f=9 g=3 h=5 i=2 solution12: a=7 b=3 c=8 d=6 e=4 f=5 g=1 h=9 i=2 solution13: a=7 b=6 c=1 d=3 e=4 f=9 g=8 h=5 i=2 solution14: a=7 b=8 c=3 d=1 e=4 f=5 g=6 h=9 i=2 solution15: a=8 b=3 c=7 d=5 e=4 f=6 g=2 h=9 i=1 solution16: a=8 b=5 c=2 d=3 e=4 f=9 g=7 h=6 i=1 However, the only "real" solutions are solution 1 and 3. Solution 2,4,5,12,13,15,16 are either reflections or rotations of solution 1. Solution 6,7,8,9,10,11,14 are either reflections or rotations or solution 3. solution1: a=1 b=6 c=7 d=9 e=4 f=3 g=2 h=5 i=8 1 6 7 9 4 3 2 5 8 solution2: a=1 b=9 c=2 d=6 e=4 f=5 g=7 h=3 i=8 1 9 2 6 4 5 7 3 8 (reflection of solution 1 along the AI-line) solution3: a=2 b=5 c=3 d=9 e=4 f=8 g=6 h=1 i=7 2 5 3 9 4 8 6 1 7 (neither rotation nor reflection of solution 1) solution4: a=2 b=5 c=8 d=9 e=4 f=3 g=1 h=6 i=7 2 5 8 9 4 3 1 6 7 (reflection of solution 1 along the DF-line) solution5: a=2 b=9 c=1 d=5 e=4 f=6 g=8 h=3 i=7 2 9 1 5 4 6 8 3 7 (rotation of solution 1 by 90° to the right) solution6: a=2 b=9 c=6 d=5 e=4 f=1 g=3 h=8 i=7 2 9 6 5 4 1 3 8 7 (neither rotation nor reflection of solution 1) (but reflection of solution 3 along the AI-line) solution7: a=3 b=5 c=2 d=8 e=4 f=9 g=7 h=1 i=6 3 5 2 8 4 9 7 1 6 (neither rotation nor reflection of solution 1) (but reflection of solution 3 along the BH-line) solution8: a=3 b=8 c=7 d=5 e=4 f=1 g=2 h=9 i=6 3 8 7 5 4 1 2 9 6 (neither rotation nor reflection of solution 1) (but rotation of solution 3 by 90° to the left) solution9: a=6 b=1 c=7 d=9 e=4 f=8 g=2 h=5 i=3 6 1 7 9 4 8 2 5 3 (neither rotation nor reflection of solution 1) (but reflection of solution 3 along the DF-line) solution10: a=6 b=9 c=2 d=1 e=4 f=5 g=7 h=8 i=3 6 9 2 1 4 5 7 8 3 (neither rotation nor reflection of solution 1) (but rotation of solution 3 by 90° to the right) solution11: a=7 b=1 c=6 d=8 e=4 f=9 g=3 h=5 i=2 7 1 6 8 4 9 3 5 2 (neither rotation nor reflection of solution 1) (but rotation of solution 3 by 180°) solution12: a=7 b=3 c=8 d=6 e=4 f=5 g=1 h=9 i=2 7 3 8 6 4 5 1 9 2 (rotation of solution 1 by 90° to the right) solution13: a=7 b=6 c=1 d=3 e=4 f=9 g=8 h=5 i=2 7 6 1 3 4 9 8 5 2 (reflection of solution 1 along the BH-line) solution14: a=7 b=8 c=3 d=1 e=4 f=5 g=6 h=9 i=2 7 8 3 1 4 5 6 9 2 (neither rotation nor reflection of solution 1) (but reflection of solution 3 along the CG-line) solution15: a=8 b=3 c=7 d=5 e=4 f=6 g=2 h=9 i=1 8 3 7 5 4 6 2 9 1 (reflection of solution 1 along the CG-line) solution16: a=8 b=5 c=2 d=3 e=4 f=9 g=7 h=6 i=1 8 5 2 3 4 9 7 6 1 (rotation of solution 1 by 180°)