Friday Puzzler -- 5 boxes

Alex Y
There are five boxes lined up in a row, numbered 1-5. One of those boxes contains a $100 bill. You are allowed to open one box, and if it contains the bill, you can keep it.

If you do not get the bill, the box is closed, and that night, the bill is moved to an adjacent box. I.e., if it was in 5 on the first day, it will be moved to 4. If it was in 2 on the first day, it will be moved to 1 or 3. Then you get to try again, and the process continues until you find the bill.

One strategy is to pick boxes at random, and it is 99% certain you would get the $100 within three weeks. But can you find a strategy that will always get you the $100 within a specific number of tries?

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