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Detect my chosen coin (Posted on 2016-01-19) Difficulty: 4 of 5
This is what I’ve told my two mathematician friends:

“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?

No Solution Yet Submitted by Ady TZIDON    
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re(3): Suggested wording for solution. | Comment 13 of 19 |
(In reply to re(2): Suggested wording for solution. by Ady TZIDON)

To repeat the example, but this time using square zero instead of square 8:

Let’s say that there are heads only on 3,7,20,61 and the "chosen" square is 0: binary XOR on HEADS{3,7,20,61} will be:

101101    (DEC 45) 

101101    (DEC 45)  XOR  000000 (DEC 0) = 101101 (DEC 45)

Flipping the coin on the 45 square (which is now an additional heads) creates a new result for B:
000000    (DEC 0)

So B knows the square labeled 0 is the one.

  Posted by Charlie on 2016-02-04 11:09:09
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