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successive whole numbers

 
 
Reply Mon 27 Mar, 2006 04:08 am
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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Type: Discussion • Score: 1 • Views: 1,283 • Replies: 2
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markr
 
  1  
Reply Mon 27 Mar, 2006 11:38 pm
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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whimsical
 
  1  
Reply Wed 29 Mar, 2006 05:25 am
There can only be numbers missing on the sides. The shape must be square.


Whim
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