as well.&quot,
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;
Interestingly, Minesweeper, Tetris,
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, and n x n sudoku also belong to the NP-complete category.
How hard is TipOver? "Is there, perhaps, a clever algorithm for coming up with a solution to a given puzzle instance?" Hearn asks. "“Probably not."
Hearn has also applied his analytic techniques to plank puzzles, invented by Andrea Gilbert (
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In this case, you have to cross a crocodile-infested swamp using only wooden planks supported by tree stumps. You can pick up planks and put them down between other stumps,
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, as long as the stumps are exactly the right distance apart. You can't let planks cross each other or intervening stumps, and you can carry only one plank at a time.
Here's a sample puzzle,
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To solve the puzzle, you start by walking across the first plank (length 1) to get to a stump. You pick the plank up, lay it down to the south, walk across it, pick it up again, lay it down to the east,
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, walk across it again,
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, pick it up again, walk across the length-2 plank, lay the length-1 plank down to the east, and so on.
It turns out that plank puzzles belong to the class of computational problems known as PSPACE-complete. Such problems are thought to be computationally harder than their NP-complete counterparts,
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"We should not be surprised that [plank puzzles] can be very challenging," Hearn says. "It can be very difficult to determine whether

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