Saturday, May 9, 2020

War General and Prisoners


A war general has captured N of you and is holding you prisoners.

He has two prison camps which are on different islands (say A and B) and those islands are connected to the main land by a flimsy bridge each.

Getting bored, the general decides to play a game with you.

"
You will all be given N distinct real numbers. Each of you can see the numbers of the other prisoners but not yours.

Once you see the numbers, you each have to independently come to me and tell which island you want to be in for the night (A or B).

Next morning I will start calling out two prisoners at a time starting with the smallest number and calling out in order. These two prisoners need to take the bridge of their island and walk towards the main land at the same time.

The bridges are flimsy, so if two prisoners walk the same bridge at the same time, the bridge will explode and so will the prison camps killing everyone who hasn't been freed yet.

If they take different bridges, they both go free and I will continue calling out two at a time.

You can decide upon a strategy before I assign numbers to you.
"

What is the maximum number of prisoners that can guaranteed to be freed?


[Solution]