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 An infinite chessboard (Posted on 2005-10-28)
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.

 See The Solution Submitted by pcbouhid Rating: 3.4286 (7 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: answer | Comment 6 of 26 |

I've never before heard the XOR operation described as

F(x,y) = 2*(x|y) - (x+y)

but it does work (at least for 99 xor 999).

Usually it's

(x|y) - (x&y)

Edited on October 28, 2005, 2:52 pm
 Posted by Charlie on 2005-10-28 14:49:56

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