The lock problem from 3.8: Suppose there were 2 locks, one with a uniform solving distribution 5 hours long, and one with a uniform solving distribution 10 hours long. Now suppose we make a new probability distribution where first we solve lock one, then lock two, in times X and Y. The probability is now (up to the time limits) X/10*Y/5. Hey look, symmetry!

Now suppose we condition on the total time being 1 hour. So X+Y=1. But there's still symmetry between X and Y. So yeah.