The Coins on a Chessboard Riddle

Difficulty	Categories	Source	I know the solution
🌶️🌶️🌶️🌶️ Extra Spicy	logic	Dorit and Aharon Hochbaum?	Yes

You and your friend have been imprisoned by an evil logician. The logician explains that tomorrow you will be put to trial…

I’ll bring you (without your friend) into a room where I have placed a chessboard. The chessboard has a coin on each of its 64 squares, each in a random orientation, either heads or tails. I will point out a particular square to you, unknown to your friend. Then you must flip exactly one coin, and no more.

After your flip your coin and exit the room, your friend may enter, and upon seeing the chessboard they must be able to determine exactly which coin I pointed out (they do not need to know which coin was flipped).

There will be no communication whatsoever between the two of you on the day of the trial. But today, you may strategize as much as you’d like.

… as per usual, correctly guessing the indicated coin is a matter of life or death!

What strategy allows you to communicate the indicated square to your friend using only a single coin flip?

Daniel’s Notes

A really excellent one, and another one that took me a very long time (years?) to solve.

Please assume that the orientation of the board itself is clear to both you and your friend upon entering.