So here’s the scenario: 100 of you are going to stand in a line, take a $1 bill (imagine for the purposes of this experiment that we all live in the US), write your position in the line up on it and then hand it over to Henry Reich from MinutePhysics.
He’ll then take his pool of marked $100 bills, mix them up and randomly put them in 100 marked boxes in a different room.
Then the game begins - each of you comes into the room one at a time and has the chance to look in 50 boxes to find your $100 bill. If you find your bill, great! Show Henry and then put the note back in the box before leaving through a different exit so you can't tell anyone else what you found.
After you, the next person will go in and try to find their note.
If all of you find your notes, then all of you win $100 (plus your original $1 back). But if even one of you can't find your note, then the game's over and Henry gets to pocket all the cash.
So would you take the bet? Before you decide, there are some rules.
1. You can only enter the room one at a time.
2. You can only look in half (50) of the boxes when you enter the room.
3. You can't alter anything in the room while you're in there.
4. Although you can talk about a strategy before you enter the room, you can't communicate with anyone afterwards.
Although it sounds like fun, the odds of all 100 of you finding your notes that way is only around 0.00000000000000000000000000000008 (or 1/2^100), so it's probably not a bet you want to take.
But it turns out there is a way to increase your odds significantly, and it's far more simple (and also mathematically genius) than you're probably thinking.