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HMMT 2004 U5

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Augustin has six 1×2×π1 \times 2 \times \pi bricks. He stacks them, one on top of another, to form a tower six bricks high. Each brick can be in any orientation so long as it rests flat on top of the next brick below it (or on the floor). How many distinct heights of towers can he make?

Dataset text NuminaMath olympiads. Quoted with source.

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