The SOMA Cube
Deep Thinking Questions
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How many unique solutions does the SOMA Cube have (excluding rotations/reflections)?
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What defines a solution as truly "unique"?
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How can you prove that two configurations are not the same under rotation or reflection?
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What mathematical or algorithmic methods could be used to count all unique solutions?
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Which faces of the final cube are always exposed? Are there parts that are never exposed?
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Can any piece never occupy a corner of the cube? Why or why not?
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Is it possible for a piece to be completely surrounded—fully internal—in any solution? If so, which one(s)?
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Could the same piece always end up in the center of the cube across all unique solutions? How would you check?
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Can the SOMA Cube concept be extended to build a 4×4×4 cube? What new rules or patterns would be needed?
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What other 3D shapes can you build using all 7 Soma pieces?
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Could a Soma-like puzzle be built to form a different solid (like a tetrahedron)?
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What new question did this activity spark for you?
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