How can this strategy work better than guessing at random? The answer has to do with cycles. The following video will explain a bit more about how cycles work.
When the numbered slips are distributed in the boxes, they are being randomly split into cycles. As long as there are no cycles longer than 5 boxes, everyone will find their number.
If a cycle is longer than 5 boxes, it will take you more than 5 turns to make a full pass through it. You only find your own number at the end of a full pass.
Every box must be in a cycle, and every cycle must start and end in the same place. As long as you start at your own number, you're guaranteed to return to your own number eventually.
Exactly! If the slips happened to be shuffled in a way that all the cycles are short, you'll win by following this strategy. If there's a long cycle, you're out of luck. Whether you win or lose following this strategy is decided when the slips are shuffled. In the next page, we'll look at how likely it is that the cycles are short enough for you to win.
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