Related to Open Problem #1: No attacks!

Logic Level 2

What is the maximum number of queens you can place on a 4 × 4 4 \times 4 chessboard such that none of them can attack each other in one move?

1 2 3 4 5

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Sharky Kesa
Nov 13, 2017

By Pigeonhole Principle, if there are 5 queens on the board, then there must exist 2 queens on the same row or column, thereby attacking each other. Therefore, there are at most 4 queens on the board, which is satisfied by

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Find the maximum number of queens that can be placed on an n×n chessboard such that no two attack one another ?

The answer is n-1 queens for n=2 or n=3 and n queens otherwise, which gives eight queens for the usual 8×8 board

and 4 Queens for this one.

Vijay Simha - 2 years, 7 months ago
Munem Shahriar
Oct 8, 2017

4 \boxed{4} is maximum.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Should this not be the m a x i m u m maximum number of squares? The minimum would be 1 1 , for one queen placed anywhere on the board cannot attack itself.

Brian Charlesworth - 3 years, 8 months ago

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