100 prisoner puzzle

The cache is not at the posted coordinates

Solve the puzzle below to unlock its real location!

Puzzle:

Say there are 100 prisoners, numbered 1 to 100. Slips of paper containing each of their numbers are randomly placed in 100 boxes in a room. One at a time, each prisoner is allowed to enter the room and is allowed to open any 50 of the 100 boxes, searching for their number. Afterwards, they must leave the room exactly how they found it when they came in. They can't communicate at all with the other prisoners after they enter the room. If all 100 prisoners find their number, they all are let free. But if even 1 of them does not find their number, they are not free. They are all allowed to strategize before they go into the room. So what is their best strategy?

If they all search for their number randomly, they have a

0.0000000000000000000000000000008% chance of everybody being able to find their number within the 50 boxes they can each open.

To put that in perspective, two people have a better chance of picking out the same grain of sand from all the beaches and deserts on earth, than to escape this way.

So how do they increase their chances?

Well you are going to have to figure out the best strategy (Yes there is a definite and correct answer to this) and then come up with the percentage they have of escaping if everybody used that method.

You can validate your puzzle solution with certitude.

Congrats to NYWanderer for being the FTS!

Congrats to hartsdale for beign the FTF!

Additional Waypoints