successive whole numbers

Forums: Riddles
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Place successive whole numbers, starting with 1, in a regular square grid, in such a way that each number equals the sum or difference of two of its neighbors (hor/vert/diag).

How far can you get?

Example upto 52:

Code:

    50 33 43 26 40 44 

 38 23 27 10 12 14 30 

 46 15  8 19  2 16 32 

 39 31  7  1  3 18 37 

 41 24  6  5  4 21 47 

 52 17 11 25  9 13 34 

 45 28 36 20 29 22 35 

       48 49 42 51

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Are there any constraints on the shape of the final grid? Can it have holes?

For instance, none of 6's neighbors require 6 to be there. It could be removed and placed on the right edge near 47 so that 53 could be added.

9 could also be removed and placed elsewhere.

Here's an infinite solution:

Code:

1 2 4 5  7  8 10 11 13 14 16 17 19 20 22 23 25 26 28 29 31 32 ...

  3 6 9 12 15 18 21 24 27 30 33 ...

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There can only be numbers missing on the sides. The shape must be square.

Whim

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successive whole numbers

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