Credit for this problem goes to jrice and rquabili. Thanks!

64 quarters

Quarters on a chess board

Unsurprisingly, this question involves a perverse jailer and two prisoners hoping to gain their freedom.

The jailer has devised the following game:

Prisoner #1 will enter into a room, where he will find a standard 8x8 chess-board and the jailer. On each square, there will be a quarter. The jailer will point to a square of his choosing, then Prisoner #1 will be forced to flip over a single quarter, but he can choose which quarter to flip.

Next, prisoner #2 will enter the same room. He gets the opportunity to point to a single square. If he points to the same square that the jailer pointed to, both prisoners survive. Otherwise… you know the drill.

Prisoner #1 and #2 can collaborate before the game begins, but once the game starts they are no longer allowed to communicate in any way.

What’s the best strategy? How likely are they to survive?