Difference between revisions of "2014 IMO Problems/Problem 2"
m (→See Also) |
m (→Problem) |
||
Line 1: | Line 1: | ||
==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 |