Logic puzzles, riddles, & maths problems

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Can you show that perfect compression is impossible?

How can 2018 monks find eternal peace?

How can a greedy pirate captain keep his treasure to himself?

Given some paper squares, can you slice them and then glue them back together to form a single square?

This problem is a really interesting problem I solved two times. The first time I solved it I failed to prove exactly how it works... then some years later I remembered the problem statement and was able to solve it properly. Let's see how you do!