Because of the way that the problem is set up (each of the 100 numbers is in one of the 100 lockers), it can always be written as a list of disjoint cycles (mat

Because of the way that the problem is set up (each of the 100 numbers is in one of the 100 lockers), it can always be written as a list of disjoint cycles (mathematically: every permutation can be written as a product of disjoint cycles). So, by starting in your own locker, you will eventually end up finding your own number. The only constraint is that everyone has to do it in 50 tries or less, i.e. there's no cycle of length >50.