Made Tough Over Easy
Many unsolved problems exist for mathematicians to play with...unfortunately, they are often so obtuse that only mathematicians can understand the mathematics needed to play with them.
But, the Collantz Conjecture comes to the rescue. It is a problem you can share with students of even a young age...and they can play with it. They may not solve it, but who knows...
Basically, the Collantz Conjecture states: Start with an integer N greater than 1. If N is even, halve it to get 0.5N. If N is odd, replace it by 3N+1. Continue doing this. If the procedure reaches 1, stop. Collantz's conjecture is that it will always stop for any integer greater than 1.
Unfortunately, despite alot of playing and number-crunching, no one has been able to prove this is true. As good evidence of its veracity, mathematicians (aided by computers) have shown that it eventually reaches 1 for all N < 1012.
I have played with the problem off and on, looking for patterns. Why don't you do the same...one never knows what you will see (that others missed)!