6 ms·

Think about how you will get back to the box you got assigned to. Like what do you have to see in order to return to box 89, where you started?

• SilasX 10y ago
  Ah, okay, that makes more sense. So the solution is to impose a random ordering on the (1-100 random numbers assigned to the) boxes that ensures you will return to the first one you picked, and that the one that points to your initial pick (or your initial pick itself) has your name in it. This ordering then partitions the boxes into cycles where each prisoner is in their cycle, and has a low chance of having 50-sized cycles. Still mesmerized at how the choice of query can improve your chances like that without accumulating information.
• foxfaction 10y ago
  But why would that matter? You don't know 89 has your name in it, because the numbers were randomly assigned to random people in the first place. You would just draw the name associated with box 89, which is not necessarily your name.
  • Tycho 10y ago
    Whatever box you open, you take the name inside and go to the number you associated with that name. So when you end up at box 89, the last box you opened must have had your name inside. So you will have found your name, provided you got there in under 50 steps.