This is ONE of the toughest of all
Geometry
Level
4
Given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces that can be reassembled to yield the second? Show your answer with proof.
No
Yes
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1 solution
This is not easy to prove. Here's a proof of why a regular tetrahedron cannot be cut up into finitely many pieces which then are supposed to reassemble into a regular cube
Dehn's Dissection Theorem
This is the Hilbert's Third Problem, one of the famous list of Hilbert's Problems
Hilbert's Problems
which are some of the most difficult problems in mathematics, some of which remain unsolved.
The title should have been "This is ONE of the toughest of all you know".