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Picking Painted Cubes

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Author: Annie Fetter
Description: active problem Geometry, difficulty level 2. A large cube, composed of smaller cubes, is painted on all sides. The edge length is five small cubes. It's then broken apart and the smaller cubes are put in a bag. What are the odds that a chosen cube is painted on three sides? two? one? none?
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Problem page: http://mathforum.org/librarypow/puzzles/index2.ehtml?puzzle=1575
Solution page: Problem #1575

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