The Collatz conjecture (3n+1 conjecture): starting from any positive integer, if even divide by 2, if odd multiply by 3 and add 1 — the conjecture states this process always eventually reaches 1. Unsolved since 1937.
The simplest unsolved problem in mathematics — every amateur can understand the question, but 85 years of work by professional mathematicians has failed to prove or disprove it. Erdős said 'Mathematics is not yet ready for such problems.'
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