as well."
Interestingly, Minesweeper, Tetris, 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 (
http://clickmazes.com/) and available as River Crossing from ThinkFun,
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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, as long as the stumps are exactly the right distance apart. You can't let planks cross each other or intervening stumps,
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, and you can carry only one plank at a time.
Here's a sample puzzle.
To solve the puzzle,
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, 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,
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, lay it down to the east, 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,
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, 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,
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," Hearn says. "It can be very difficult to determine whether

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