There are three players, Alice, Bob, and Carol playing against a referee. The referee poses a question ∈ ∈ { 0 , 1 } to each of the players. The three players each respond with an answer ∈ ∈ { 0 , 1 } . The referee draws three questions x, y, z uniformly from the 4 options { ( 0 , 0 , 0 ) , ( 1 , 1 , 0 ) , ( 1 , 0 , 1 ) , ( 0 , 1 , 1 ) } . As a clarification, if question triple ( 0 , 1 , 1 ) is chosen, then Alice receives bit 0, Bob receives bit 1, and Carol receives bit 1 from the referee. Based on the question bit received, Alice, Bob, and Carol each respond with an answer a, b, c also in the form of 0 or 1. The players can formulate a strategy together prior to the start of the game. However, no communication is allowed during the game itself.