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Upstart Puzzles: Ice Trap

Ice Trap, illustration

Credit: Andrij Borys Associates / Shutterstock

Imagine a 500-square-by-500-square red/black ice checkerboard with walls along all four edges. A frictionless hockey puck is moving diagonally above the checkerboard in a northwest, northeast, southeast, or southwest direction (you do not know which or where the puck started) at a speed of one diagonal square in each time unit. And you want to trap it in a one-square-by-one-square location.

You can put up horizontal (east-west) or vertical (north-south) walls of any length across the checkerboard, but your total wall length is limited to some total T. In order to build your first wall of length L, you must wait at least ceiling (L/10) time units from the start of the game. To build any subsequent wall of length L′, you must wait at least ceiling (L′/10) time units from the time you built your last wall. Once you are allowed to put up a wall, it appears instantly. You may likewise tear down your built walls instantly at any time. If, as you attempt to put up a wall, the puck is in one of the squares the wall covers, then the wall will not be built (and you will be told the wall would have hit a puck). You can build a new wall after L/10 further time units.


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