On one hand, the 3x+1 problem is very simple since it only takes an understanding of arithmetic to grasp. On the other hand, it remains one of the most elusive open (unsolved) problems in mathematics. It goes like this: Take any positive integer. If your integer is odd, multiply it by 3 and add 1 ("3x+1 it"); if your integer is even, divide it by 2. You now have a different positive integer. If it is odd, 3x+1 it; if it is even, divide it by 2. Continue this process until you get 1 (if that ever happens). For example, starting with seven gives the following sequence of numbers:
7 >> 22 >> 11 >> 34 >> 17 >> 52 >> 26 >> 13 >> 40 >> 20 >> 10 >> 5 >> 16 >> 8 >> 4 >> 2 >> 1
Here is another:
6 >> 3 >> 10 >> 5 >> 16 >> 8 >> 4 >> 2 >> 1.
It is conjectured (believed) that no matter what number you start with you will always get 1 eventually. However, no one can prove that this is true! Can you? Or maybe you can find a number that doesn't eventually give you 1. Either way you would become very famous!