savoy082

Today's problem has gotten me thinking about it several times for several reasons. In particular, the first time I came across it I was pretty sure I knew the answer but didn't really know how to formalize a proof. It was only a couple of years later, when I remembered the problem for no reason at all, that I was able to answer it completely. Problem statement: imagine you have an infinite table with a checkerboard pattern. 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? The key is in understanding that the $1997$th row and the $2018$th column have nothing special. Hint 1 Write down a small board and fill it in following the rule of the problem statement. Look for...