All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
An infinite chessboard (Posted on 2005-10-28) Difficulty: 2 of 5
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: ( You must be logged in to post comments.)
  Subject Author Date
SolutionA proof!Ken Haley2005-11-09 00:32:51
re: Amazingpcbouhid2005-11-04 06:27:40
AmazingKen Haley2005-11-04 01:03:07
re: answerJosh706792005-10-31 12:40:54
re: What?pcbouhid2005-10-31 06:09:05
nvmdaniel2005-10-31 00:31:57
answerdaniel2005-10-31 00:28:10
What?Alex Korn2005-10-30 21:15:31
re(4): About XOR - only topcbouhid2005-10-30 12:29:32
re: QuestionCharlie2005-10-29 16:48:48
QuestionQuestionBractals2005-10-29 16:35:59
re: bitwise XORCharlie2005-10-29 09:38:27
re(3): About XOR - only toCharlie2005-10-29 09:35:02
re(2): About XOR - only topcbouhid2005-10-29 07:41:53
re: About XOR - only toCharlie2005-10-28 23:52:30
About XOR - only to "dynos"pcbouhid2005-10-28 20:27:18
Some ThoughtsXOR symbolFederico Kereki2005-10-28 17:53:47
re: bitwise XORJosh706792005-10-28 16:18:03
bitwise XORSilverKnight2005-10-28 15:01:46
re(2): answerJosh706792005-10-28 14:54:54
re: answerCharlie2005-10-28 14:49:56
Solutionre: neat -- and the snake returnsCharlie2005-10-28 14:44:51
SolutionanswerSilverKnight2005-10-28 14:34:43
Solutionthe trickJosh706792005-10-28 13:27:23
re: neatpcbouhid2005-10-28 13:22:21
Some ThoughtsneatJosh706792005-10-28 13:07:38
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information