My reference is to the N-Queens problem, which consists of N queens to be placed on an NxN chess board in such a way that no queen attacks any other queen. This problem is being solved by using backtracking approach.
On the Wikipedia page of https://en.wikipedia.org/wiki/Eight_queens_puzzle#Counting_solutions, it is mentioned that:
"Note that the six queens puzzle has fewer solutions than the five queens puzzle."
Why is it so? In every other case, the number of solutions rises as the number of queens rises.
I want an answer that I can use to explain satisfactorily to an external examiner for vivas on this particular topic. Hence, an answer using logical and simple grammar would help.
Thanks.
