Today’s four puzzles are inspired by chess. (If you haven’t yet watched the recent documentaries on Judit Polgár and Hans Niemann, I recommend them.)
1. Oddities
1. A chess tournament is taking place with several participants. Not every player played against every other player, and some players may have played many more games than others.
Some of the players played an odd number of games. Prove that the number of such players must be even.
2. L of a trip
A knight in chess moves in an “L” pattern – two squares in one direction and one square in a perpendicular direction. Starting in the bottom right corner of a regular 8×8 chessboard, is it possible for a knight to visit every square on the chessboard exactly once and end up in the top left corner?
3. Pawn return
Take a chessboard with the standard initial setup of pieces. What’s the fewest number of moves needed for a pawn to leave its initial place, get promoted/queened, and then return to its original position?
(Assuming the two players are collaborating to achieve this, not that the one is scuppering the other).
4. Four knights
Show how to swap the two pairs of knights on the following strangely-shaped grid.
The knights make one move at a time. You’re trying to get the black nights to where the white knights are, and the white knights to where the black knights are.
If you try to solve this problem using knights on a physical grid, you will get very confused. Try to think abstractly. With one simple(ish) insight, the problem is quickly solvable.
I’ll be back at 5pm UK with the solution.
PLEASE NO SPOILERS. Instead – discuss chess!
Today’s puzzles come from We Solve Problems, a charity that runs free maths circles for secondary school pupils (years 7 to 11) between September and May in more than a dozen cities across the UK. A maths circle is a social club for maths-loving children, led by post graduates and PhD students. You can register now for the next school year.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
