The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence.
1,000Assuming the Collatz conjecture is false, how long would any alternative stopping cycle have to be?
Wikipedia says "The length of a non-trivial cycle is known to be at least 186265759595", so don't bother looking for it by hand 😁
@April i am open to the idea that something like 25% is a reasonable place for this market to be at but i think it would require having some particular reason to believe we might be sorta close. it's a famous problem that's nearly a century old, outside-view we probably don't solve it in this particular decade
Wherever I see this problem I feel that if I'd just spend five more minutes thinking about it I'd figure it out...
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What is this?
What is Manifold?
Are our predictions accurate?
Why use play money?
Why use play money?