The retrograde analysis of a game is the analysis of what happened in order to reach a particular state of play. There’s a large literature about this sort of problem in chess.
Today’s first puzzle is retrograde analysis of snakes and ladders.
1. Brand new it’s retro
Three young children, Red, Green, and Blue are playing snakes and ladders. They are called away, leaving the board, including the die, as below. The die is showing the last number rolled.
Deduce whose turn it now is, and the order of play.
Some clarifications about the rules of snakes and ladders that the kids are playing.
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The game starts with each player putting their marker on 1.
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Each player roles a single die. If you roll a 6, you get an extra throw.
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The players take turns in a fixed order.
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You go up ladders, and down snakes. It is possible to go up two ladders, or down two snakes, or up a ladder and down a snake on the same turn.
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The winner is the player who lands exactly on 100. (If you are on 98 and roll a 3, you ‘bounce back’ and land on 99.)
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If a player lands on a square occupied by another player, the player is not sent back to square 1.
I’ll give you one hint: the game that was played was rather extreme – a lot of 6s were rolled!
The snakes and ladders puzzle was created by Ammar Fathin Sabili, an Indonesian who is studying for a PhD in computer science at the National University of Singapore.
He also composed the following puzzle:
2. The missing symbol
What symbol would fit perfectly in the centre of this logo?
Each of the statements describes the symbol neatly. (One of the statements requires knowledge of mathematical notation, but the other three don’t.)
I’ll be back at 5pm UK with the answers to both puzzles. Meanwhile, NO SPOILERS.
Instead discuss board games.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
