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a) Place numbers 1 to 25 on the cells of this board so that each of them, except for 1 and 2, is the sum of two of its (up to 8) neighbors in at least one way.

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b) Do likewise with the numbers 1 to 36 in a 6 x 6 board? ¿Can a similar outcome be achieved in a square board of any larger size?

Puzzle due to Giulio Cesare.

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2 Answers 2

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For a:

 25 24 17 23 22
 16  9 15  8 14
 19  7  2  6 20
 12  5  3  4 10
 18 13  1 11 21 

Or if each number must be doable in exactly one way:

 25 24 15 23 20
 16  9 17  6 14
 19  7  2  4 10
 12  5  3  1 21
 18 13  8 11 22 

For b:

 32 33 18 26 19 31
21 11 1 7 12 29
34 10 4 3 9 17
24 16 6 2 5 25
30 14 8 13 15 20
36 22 27 23 28 35

(found via computer search. Searching for a 7x7 found no solutions, even under the laxer "sum of two neighbors, in at least one way" rule)

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  • $\begingroup$ So solutions for larger boards (say 8 x 8) not likely? $\endgroup$ Mar 28 at 17:12
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a)

enter image description here

b)

There's a 30 character minimum for a post

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