How are there unsolved math problems?
In: 9
Here’s a simple one to understand:
Pick a number (non-negative, no decimals).
1. If it’s even, divide it by half.
2. If it’s odd, multiply it by 3, then add 1.
Keep repeating these steps with the new numbers you get.
You’ll notice that once you reach 4, the next numbers in the sequence are 2, then 1, then 4, then 2, then 1, and so on. From there, it loops forever.
**The question is:** will you always reach this loop with any starting number you pick?
This is called the [Collatz conjecture](https://en.wikipedia.org/wiki/Collatz_conjecture) and has remained unsolved for almost 100 years.
These are what unsolved math problems look like. They’re not equations that need solving, they ask a question which needs an answer and a proof of the answer.
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