Everyone loves brain teasers, but especially deceptively simple ones (deceptively-full-of-calculus problems aren't very fun) that are so intuitive, first graders often outperform adults—but what about ones mathematicians can't solve? The "3X+1 Problem," aka the "Collatz Conjecture," drives mathematician so bonkers it once was thought to be a Soviet plot to distract scientists from their work.
Anyone with a solid grasp of addition, division, multiplication can try it and anyone can see it in action—but no one can explain it, prove it, or disprove it. Tipping Point Math demonstrates it in this video, "The Simplest Impossible Problem," but a written explanation will be attempted below.
You start with a positive whole number and follow two simple rules: if the number is even, divide it by two; if the number is odd, multiply by three and add one.
After doing that, you apply the same rules to the result of the first number. So, if we start with 10, the next number is 5. Then you apply the rules again, this time applying the odd number rule (3N+1) to get 16. Divide by two for eight, again for four, again for two, and finally for one.