Month: April 2023

One of our favourite chess puzzles …

Place 8 queens on a chessboard such that none of the queens can take any of the others. Above is a fail – only 5 queens are on the board and they are no places left to put any more.

Here is a website to try yourself to fit 8 queens on the board, it is possible!

We then looked at changing the size of the board from an 8 by 8 to smaller sizes, e.g. can you fit 5 queens on a 5 by 5 board? And if so, how many “unique” solutions are there? We defined a unique solution as being one that did not look like any others we had found when we rotated our paper or put it up to the light so it appeared flipped! Here are our solutions for 5×5, 6×6 and 8×8.

There is a great numberphile video  on this puzzle, and all the answers and stats you could want here.

And finally this great puzzle from Alex Bellos in the Guardian

Can you create a sudoku?

Think about

• What would be an efficient way to create a puzzle?
• How difficult would you like it to be?
• What is the maximum number of 3×3 squares you could remove and it still be solvable? Does it matter which squares?
• Could you design it so that it could be easily transformed into mutliple versions? How many versions could be created from your one puzzle?
  

Here is a fascinating article on how one website generates their sudokus and a paper proving the minimum number of clues needed.