Toads and Frogs Puzzle

Toads and Frogs Puzzle

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The Board

Toads and Frogs is played on a 1-by-N grid.

The Pieces

There are X toads and Y frogs (X+Y≤N). At the beginning of the puzzle, the toads occupy the leftmost X slots of the grid, the frogs occupy the rightmost Y slots of the grid, and the other slots are empty.

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Rules

To move: Toads move to the right and frogs move to the left.

A toad may move to the right one space if that space is unoccupied. If one space to the right of a toad there is a frog, and two spaces to the right of the toad there is an unoccupied slot, then the toad may hop over the frog into the unoccupied slot.

A frog may move to the left one space if that space is unoccupied. If one space to the left of a frog there is a toad, and two spaces to the left of the frog there is an unoccupied slot, then the frog may hop over the toad into the unoccupied slot.

The puzzle is solved after the frogs and toads are moved so that the frogs occupy the leftmost Y spaces and the toads occupy the rightmost X spaces.

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