In Harry’s experience once of the challenges that ChatGPT handles least well is Chess. Not the game, but the board. Ask it to render a nice drawing of a chess board and it returns a Grandmaster’s nightmare. Wrong number of rows, wrong number of columns. Pieces all awry and very often the black and white squares are jumbled out of place. Some things are better left unseen, however it does remind me of a famous magic trick that forms the basis for this week’s puzzle. I have taken the account from the Group Theory lecture notes at Southampton, but there are other versions around the web. See if you can work out how the puzzle is done without looking up the solution!
Reindeer
Last week’s puzzle was a simple parity problem. If the door number was not a square then its factors come in pairs so its state get’s switched an even number of times, ending up closed, but if it IS a square number then it is switched an odd number of times and is open at the end. Their are precisely nine numbers in the range 1-99 that are squares: 1,4,9,16,25,36,49,64,81. I leave it to you to decide which stall contained which Reindeer!