Difference between revisions of "2014 IMO Problems/Problem 2"
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==Problem== | ==Problem== | ||
| − | Let <math>n\ge2</math> be an integer. Consider an <math>n\times n</math> chessboard consisting of <math>n^2</math> unit squares. A configuration of <math>n</math> rooks on this board is <math>peaceful</math> if every row and every column contains exactly one rook. Find the greatest positive integer <math>k</math> such that, for each peaceful configuration of <math>n</math> rooks, there is a <math>k\times k</math> square which does not contain a rook on any of its <math>k^2</math> squares. | + | Let <math>n\ge2</math> be an integer. Consider an <math>n\times n</math> chessboard consisting of <math>n^2</math> unit squares. A configuration of <math>n</math> rooks on this board is <math>\textit{peaceful}</math> if every row and every column contains exactly one rook. Find the greatest positive integer <math>k</math> such that, for each peaceful configuration of <math>n</math> rooks, there is a <math>k\times k</math> square which does not contain a rook on any of its <math>k^2</math> squares. |
==Solution== | ==Solution== | ||
Revision as of 05:47, 9 October 2014
Problem
Let 
be an integer. Consider an 
chessboard consisting of 
unit squares. A configuration of 
rooks on this board is 
if every row and every column contains exactly one rook. Find the greatest positive integer 
such that, for each peaceful configuration of rooks, there is a 
square which does not contain a rook on any of its 
squares.
Solution
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
| 2014 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 2 |
| All IMO Problems and Solutions | ||
