Six men are queuing in the bank when the clerk decides to take a break for 10 minutes! Before leaving, he gives to the six men a numbered ticket, in the same order of the queue (ticket #1 to the first man, #2 to the second, etc.).
After a while, when the clerk returns, the men become terribly confused and start pushing each other to become the first in line, not worried about their tickets.
Trying to calm down the men, the clerk says, "Stop! Let's make a game! There is a chance that all of you will receive twice the money you're asking, but otherwise you won't get anything! Let me explain the rules.
"The last person in the queue at this moment checks his ticket number. If it's not 6 (in which case the game immediately ends), he occupies the position suggested by his ticket. Then, whoever was previously standing in that position checks his ticket, too. If it's 6, he goes to the end of the queue and the game ends, but otherwise he goes to the position indicated by his ticket, and so on. The game ends when someone, looking at his ticket, goes to the sixth position. You win the money only if, at the end of the game, you're all in the correct positions as indicated by your tickets."
What's the probability that the six men get double the money?
Example: The sixth man looks at his ticket and reads 4, so he goes to the 4th position. Now the man who previously was 4th looks at his ticket and reads 6, so he occupies the last position. In this case, they win only if the men occupying the first, second, third and fifth position already were in the correct position (ergo they respectively had the tickets 1,2,3,5).