“Imagine a 64-square chessboard with a coin on each square.
Each of the coins has either head or tails facing up, chosen at random.
I check the board and decide which coin will be my favorite one.
One of you (say A) will be with me, see the chessboard and I will reveal to him (only to him) which coin is my favorite. He then must flip over exactly one of the coins on the chessboard, while the other mathematician (B) is in another room not looking.

Once the coin is flipped over, the uninformed mathematician (B) is summoned into the room and must deduce which coin is my favorite only by examining the coins on the chessboard.
To secure absence of any other hints A is escorted out of the room.

Clearly, prior to the procedure, you are free to discuss the problem between the two of you and establish its solving strategy. You have no time limit, you are free to use any kind of calculator, but any communication between you two is strictly prohibited”

What strategy can the two mathematicians devise to ensure that my favorite coin can always be correctly identified?

Actually my point was slightly different.

After getting Ady's useful hint about 'devil's chessboard' I was able to do some checking.

In that problem, the wording is something like 'A then may flip over exactly one of the coins...' whereas here it is 'A then must..'

So another way of putting my point is 'Can the devil ever select a configuration of coins and a favourite coin such that A, being compelled to flip a coin, cannot communicate the favourite coin to B?'

The forums seemed to be a bit vague on this, which is why I asked.