Mermin-Peres Magic Square Game









Instructions and Rules


Introduction

The Mermin-Peres magic square game is a game played by two players: Alice and Bob. They like to play this game a lot and we will play multiple instances, i.e. rounds of the game. In each round of the game Alice and Bob will receive a challenge from a judge. Depending on their answers, they will either both win or both lose. The players are allowed to agree on a strategy prior to the game, however once the game has started they cannot communicate anymore: i.e. they must try and coordinate without communication, even instantaneously.

Sequence of the game

  1. This game involves a 3 x 3 matrix

  2. Alice and Bob decide a pre-game strategy which they will be using during the game. They are not allowed to communicate at any point during the game.

  3. The Judge assigns a row number to Alice and a column number to Bob.

  4. Alice has to fill the assigned row with zeroes and ones, in such a way that there are even number of ones in that row.

  5. Bob has to fill the assigned column with zeroes and ones, in such a way that there are odd number of ones in that column.

  6. Both Alice and Bob submit their solution to the Judge

  7. Alice and Bob win if they agree on the value of the cell belonging to the intersection of Alice's row and Bob's column. They lose otherwise.

Features of the game

Getting started