The squares of an infinite chessboard are numbered successively as follows: in the lower left corner (first row, first column) we put 0 (zero), and then in every other square we put the smallest nonnegative integer that does not appear to its left in the same row or below it in the same column. See it partially filled:

            |   |   |   |   |   |   |   |   |
            +---+---+---+---+---+---+---+---+--
            | 5 |   |   |   |   |   |   |   |
            +---+---+---+---+---+---+---+---+--
            | 4 | 5 |   |   |   |   |   |   |
            +---+---+---+---+---+---+---+---+--
            | 3 | 2 | 1 |   |   |   |   |   |
            +---+---+---+---+---+---+---+---+--
            | 2 | 3 | 0 | 1 |   |   |   |   | 
            +---+---+---+---+---+---+---+---+--
            | 1 | 0 | 3 | 2 | 5 |   |   |   |
            +---+---+---+---+---+---+---+---+--
            | 0 | 1 | 2 | 3 | 4 | 5 |   |   | 
            +---+---+---+---+---+---+---+---+--

Find the law that rules the numbers that fills the chessboard, so that in seconds, you can evaluate the number that is, for example, in the intersection of the 1000th row and the 100th column.

(In reply to re: About XOR - only to by Charlie)

Tk, Charlie. There was another mistake that I remembered later: "exclusive or" was denoted by "XR" not "XC". "XC" was (is?) the common "OR".

Posted by pcbouhid on 2005-10-29 07:41:53