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This is a solved, filled table. I'm trying to understand how it was put together. Numerically, the first half of the chart is easy to figure out, (The parts in red are resultant in simple addition.) But I can't figure out how to actually solve for the bottom half. There must be some simple way to get those numbers, but I can't figure out how it was done.

The Chart

EDIT: The 9 row was incorrect, see the new image. Each row should only have one of each number.

Em.
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zan
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    How is this real analysis? – Brian Tung Jan 13 '16 at 21:10
  • Sorry, I don't know what to tag it. – zan Jan 13 '16 at 21:11
  • Where is it from? That might provide a hint. Note that the black numbers are not symmetric and that the numbers in the border do not appear in the row/column they are in except the 8 column. The 4 column and 9 row are the only ones that have duplicate entries that I see. – Ross Millikan Jan 13 '16 at 21:14
  • It's an item combination table from a game. In this case, there are a total of 9 different items that can be made. Any one item can be made with a combination of 2 different items. The table shows the result.

    EDIT: The 9 row was incorrect, see the new image. Each row should only have one of each number.

     – zan Jan 13 '16 at 21:18
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    It's still not symmetric. – Brian Tung Jan 13 '16 at 21:24
  • What do you mean? – zan Jan 13 '16 at 21:30
  • I meant that the table still wasn't symmetric (the ninth row was not the same as the ninth column). It is now. I tried reloading, too, although perhaps my browser is partly to blame. – Brian Tung Jan 13 '16 at 22:03
  • IMO this question is quite about mathematics. It is asking to find the pattern in an arrangement of numbers. –  Jan 14 '16 at 08:41

2 Answers2

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The left-top $9\times9$ square (headers inclusive) is filled with rotations of $912345678$.

The bottom row and rightmost column repeat the hidden diagonal elements (every other digit in $\color{gray}91\color{gray}23\color{gray}45\color{gray}67\color{gray}89\color{gray}12\color{gray}34\color{gray}56\color{gray}78\color{gray}9$).

enter image description here

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If it's from a game I imagine it's a conditional thing. Rules can be as follow:

1) a = b is not allowed

2) if neither a nor b are equal to nine => a + b modulo 9 (with 9 representing the 0= 9 residue class); red if a + b $\le$ 9; black if a + b > 9.

3) if a = 9 => black (2 * b) modulo 9.

4) if a = 9 and b $\ge$ 7 => +1 bonus point.

fleablood
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