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# Collatz Like Problem Watch

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1. Let be a function over positive integers such that
1. .
2. if is even.
3. if is odd.

Prove that is always for any .
2. Not sure how mathematical the proof needs to be but...

All even numbers will reduce to 1 according to Law 2.
All odd numbers will become even numbers according to Law 3.
Therefore all odd numbers will reduce to 1.

Edit: nvm i'm a dumbass lmao
3. (Original post by esrever)
Let be a function over positive integers such that
1. .
2. if is even.
3. if is odd.

Prove that is always for any .
What have you tried? How far have you got? Details!

If you're struck for an approach, strong induction would be a good one to try.
4. (Original post by ghostwalker)
What have you tried? How far have you got? Details!

If you're struck for an approach, strong induction would be a good one to try.
This is an easier version of INMO 2016. I've solved it already.

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