## 100 Pots Puzzle

About a year and a half ago I presented the 100-pots puzzle, which is by far my favorite programming/logic/math problem I have ever come across. It took me a while to solve it the first time I heard it (most of the work day which is where I heard it). I also was at an advantage because the solution comes from a field of math I have particular expertise in, so most people will probably have a harder time solving it.

I don’t think anyone was able to solve it last time I presented it, and had to give the official answer, I could be wrong, I need to dig up the thread. @Absinthe however did write a simulation for it in python after I had posted the answer.

Anyway here is the problem for anyone who wants to take a stab.

All answers or hints must be CW’ed

### No tricks

First off some background. The problem is not a trick question, as much as it may seem like one. There is no play on words, no hidden exception. Everything in this problem is exactly how it is presented and the answer doesnâ€™t rely on any slight of hand. Take this puzzle at face value.

### The Puzzle

There is a room with 100 jars with lids on them all in a row. There is also a stack of papers, 100 papers each labeled 1 to 100. The papers are shuffled and one paper placed into each pot randomly.

You and your assistant are in an a joining room. Your assistant is allowed to enter the room, look in all 100 pots, and if they wish they can pick any 2 pots and switch the paper in them. They can only do this one time, they do not have to do this they can choose to also do nothing. At this point they leave the room, without talking to you.

Next, someone tells you a random number from 1 to 100. Your goal is to enter the room and open a pot that has that number in it. You are allowed to open, at most, 50 of the pots.

Whatever process you use to open those pots must guarantee that by the time you open the 50th pot that the number you were given will be found. Obviously your assistant didnâ€™t know what the number is at any point.

What rules do you give your assistant, and what rules do you follow, to ensure you are successful?

@freemo Is it that the 50th pot is the one that has to have the exact number? Or can I get the required number beforehand.

@Zach777 You can get it beforehand. You just need to get your number within 50 tries or less.

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