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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: bitwise XOR | Comment 15 of 26 |
(In reply to bitwise XOR by SilverKnight)

It's unfortunate that C uses ^ to represent xor, as Basic, and the character notations used on this site use ^ to represent exponentiation, the pointing upwards more indicative of the superscript than C's **.

BTW, also unfortunately, and I'm sure inadvertently, this whole thread is giving away the answer in the subject line.

 Posted by Charlie on 2005-10-29 09:38:27

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