jasen 4 Posted October 10, 2016 Report Share Posted October 10, 2016 [0,1,6,4,3] [4,5,6,0,9] [9,9,0,1,1] [1,0,4,5,6] [7,6,4,9,0] This 5x5 table has unique properties. Each number in a cell means : The cell = last digit of (sum of its neighbour (including diagonals)) or The cell = The remainder of the sum of its neighbour divided by 10 Here is another example [0,1,6,4,8] [1,2,1,3,2] [1,0,9,0,1] [4,5,6,0,4] [4,5,1,0,9] [6,5,9,5,6] [4,4,0,6,6] [3,3,0,7,7] [5,5,0,5,5] [1,0,4,5,1] [1,0,9,5,6] [9,0,1,0,9] [2,1,4,4,0] [8,7,9,8,9] [4,5,1,5,4] What surprised me is, every table like this will follow this : The middle cell is always 0. Any other cell (i,j), (6−i,6−j) adds upto 0 modulo 5 , that means, (i,j) + (6−i,6−j) is completely divisible by 5. I have checked this with my computer. Why this happens ? Quote Link to post Share on other sites

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## jasen 4

This 5x5 table has unique properties.

Each number in a cell means :

or

Here is another example

What surprised me is, every table like this will follow this :

I have checked this with my computer.

Why this happens ?

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