Take any positive integer. If even, halve it. If odd, triple it and add one. Repeat. Every number tested reaches 1. No one can prove this always works.
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Depth
14
Branch angle
18
Starting number
Range (1 to N)
1000
Paul Erdos said of the Collatz conjecture: "Mathematics is not yet ready for such problems." That was in the 1980s. It remains unsolved.