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This is impossible for any convex shape, so one will need to exploit the non-convexity of a bagel. The first cut needs to be such that two u-shapes are left. This is achieved best if the cutting plane is tilted with respect to the planes of symmetry of the bagel. Now, stack the two u-shapes and cut them both into three pieces using 1 cut, cutting of the 'legs' of the u's. Now we have 6 pieces and 1 cut to go, so stack all the pieces and cut right through to give 12 pieces in three cuts.

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Q: How can you cut a bagel into 12 pieces with 3 straight cuts?
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