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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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2x2 | Comment 3 of 19 |
For a 2x2 square there are 16 different coins positions. It's possible to deliver a table like this (x=head y=tail):

(x,x,y,x) position means the chosen coin is in square 3 (tail). (y,y,y,x) means the chosen coin is in square 4 (head).

(xyxy or yxyx) means coin square 1 chosen
(xxyy or yyxx) means coin square 2 chosen
(xyyx or yxxy) means coin square 3 chosen
(xxxx or yyyy) means coin square 4 chosen

F.e. With a coin distribution (1010) and chosen coin =square2 mathA should move to (1011), so mathB can consider the pattern (xyxx) and grab from there that the chosen coin is in square 2; with (0100) should move to (1100) with pattern (xxyy) and so on.

But this is not going to work for wider squares...
Edited on January 24, 2016, 4:09 pm
  Posted by armando on 2016-01-24 11:06:18
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