Retrograde analysis of the classic board game
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.
The game starts with each player putting their marker on 1.
Each player roles a single die. If you roll a 6, you get an extra throw.
The players take turns in a fixed order.
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.
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.)
If a player lands on a square occupied by another player, the player is not sent back to square 1.
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