The players win if a ⊕ ⊕ b ⊕ ⊕ c = x ∨ ∨ y ∨ ∨ z , where ∨ ∨ indicates OR condition and ⊕ ⊕ indicates summation of answers modulo 2. In other words, the sum of three answers has to be even if x = y = z = 0 . Otherwise, the sum of answers has to be odd.