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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)

 Subject Author Date A proof! Ken Haley 2005-11-09 00:32:51 re: Amazing pcbouhid 2005-11-04 06:27:40 Amazing Ken Haley 2005-11-04 01:03:07 re: answer Josh70679 2005-10-31 12:40:54 re: What? pcbouhid 2005-10-31 06:09:05 nvm daniel 2005-10-31 00:31:57 answer daniel 2005-10-31 00:28:10 What? Alex Korn 2005-10-30 21:15:31 re(4): About XOR - only to pcbouhid 2005-10-30 12:29:32 re: Question Charlie 2005-10-29 16:48:48 Question Bractals 2005-10-29 16:35:59 re: bitwise XOR Charlie 2005-10-29 09:38:27 re(3): About XOR - only to Charlie 2005-10-29 09:35:02 re(2): About XOR - only to pcbouhid 2005-10-29 07:41:53 re: About XOR - only to Charlie 2005-10-28 23:52:30 About XOR - only to "dynos" pcbouhid 2005-10-28 20:27:18 XOR symbol Federico Kereki 2005-10-28 17:53:47 re: bitwise XOR Josh70679 2005-10-28 16:18:03 bitwise XOR SilverKnight 2005-10-28 15:01:46 re(2): answer Josh70679 2005-10-28 14:54:54 re: answer Charlie 2005-10-28 14:49:56 re: neat -- and the snake returns Charlie 2005-10-28 14:44:51 answer SilverKnight 2005-10-28 14:34:43 the trick Josh70679 2005-10-28 13:27:23 re: neat pcbouhid 2005-10-28 13:22:21 neat Josh70679 2005-10-28 13:07:38

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