Why the world's toughest maths problems are much harder than a chess puzzle

The n-queens completion puzzle is a form of mathematical problem common in computer science

The above picture shows a chessboard with two queens placed on it. As the queens do not share the same row, column or diagonal of the chess board they are not attacking each other. Can you place another six queens on the board so that none of the eight queens are attacking each other? And if it’s possible, how many ways are there to do it?

This illustrated puzzle using a typical chessboard, an example of what is called the 8-queens completion problem, is from 1850. Yet only now, in a paper written by Chris Jefferson, Peter Nightingale