How Many Queens?

Logic Level 1

How many queens can be placed on an $8\times 8$ board such that no two queens are in the same row, column, or diagonal path?

The answer is 8.

5 solutions

Dan Tsaranou
Oct 6, 2015

Since a queen's domain includes her entire row and column, each time we place a queen, there can be no more queens in either that row or that column. Thus, there is a maximum of 8 queens. To show that 8 queens is attainable, check out the following placement:

Hi dan! board you have made is 10 x 10 boeard

abhideep singh - 5 years, 8 months ago

your solution was for 10x10 board not 8x8 board.

Amani Ariffin - 5 years, 8 months ago

if not mistaken there's only 7 queens could be placed in 8x8 board.

Amani Ariffin - 5 years, 8 months ago

OOPS! Here's a good solution:

Vivek Bhupatiraju - 5 years, 8 months ago

there is a youtube video by a channel numberphile on 8 queen problem

Swarang Pundlik - 5 years, 8 months ago

thank you. now i see, it make sense.

Amani Ariffin - 5 years, 7 months ago

Yes, 8 is the correct answer. The problem of finding these arrangements of 8 queens that satisfy the problem's requirements is a very famous problem called the Eight Queens Problem . It is classical problem in CS and is generally taught as an introduction to recursion.

Vivek Bhupatiraju - 5 years, 8 months ago