Think of a number. If it's even, halve it, if it's odd, triple it and add one. Now do this with the new number. Eventually you'll reach one. It takes eight goes starting from the number 6: 6 is even, so halve it, to get 3. 3 is odd, so triple it and add one, to get 10. And so on, through 5, 16, 8, 4, 2 to 1.

What's odd about this game is that it's hard to predict before you start how many goes a number will take before it gets to one. In fact the quickest way to find out for a given number is to actually do it -- there's no shortcut. Some small numbers take suprisingly many goes. Here's n excel plot of starting numbers along the bottom with the goes up the side, up to a starting number of 10,000.