This post's problem is a really interesting problem I solved two times. The first time I solved it I failed to prove exactly how it works... then some years later I remembered the problem statement and was able to solve it properly. Let's see how you do!

Problem statement

Take a chessboard and extend it indefinitely upwards and to the right. In the bottom leftmost corner you put a \(0\). For every other cell, you insert the smallest non-negative integer that hasn't been used neither in the same row, to the left of the cell, nor in the same column, below it. So, for example, the first row will have the numbers \(0, 1, 2, 3, \cdots\). What is the number that appears in the \(1997\)th row, \(2018\)th column?

Give it some thought... my best advice would be for you to create a grid in your piece of paper and start filling it out as stated by the rules. Can you find a pattern?

If you need any clarification whatsoever, feel free to ask in the comment section below.


You can read the solution here to compare with your own solution.

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