The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 0, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 4, moves by putting its piece(1) in column, 3 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 The reasonable moves for Black are to move in columns, 1, 2, 3, 4, 5, 6, 7 if Black moves in column, 1, then the position is 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 3, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 3, moves by putting its piece(1) in column, 1 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 The reasonable moves for Black are to move in columns, 2, 3, 4, 5, 6, 7 if Black moves in column, 2, then the position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 2, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 2, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in column, 5 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 2, 0, 2, 0, 0, 2 2, 1, 0, 1, 1, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 3, 5 -------------------------------------------------- if Black moves in column, 3, then the position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 2, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 2, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in columns 3, 6 We will only prove it for column, 3 Red can win in , 2, moves by putting its piece(1) in column, 3 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 1, 2, 0, 0, 2 2, 1, 2, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 4, 6 -------------------------------------------------- if Black moves in column, 4, then the position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in columns 3, 5 We will only prove it for column, 3 Red can win in , 2, moves by putting its piece(1) in column, 3 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 1, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 2, 5 -------------------------------------------------- if Black moves in column, 5, then the position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 2, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 1, moves. Indeed -------------------------------- The position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 2, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 1, moves by putting its piece(1) in column, 5 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 1, 0, 2 2, 1, 0, 1, 2, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red obviously won! -------------------------------------------------- if Black moves in column, 6, then the position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 2, 2 from which Red can win in, 1, moves. Indeed -------------------------------- The position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 2, 2 Red can win in , 1, moves by putting its piece(1) in column, 6 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 1, 2 1, 1, 2, 2, 1, 2, 2 Red obviously won! -------------------------------------------------- if Black moves in column, 7, then the position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 2 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 2 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in columns 3, 5 We will only prove it for column, 3 Red can win in , 2, moves by putting its piece(1) in column, 3 leading to position 1, 0, 0, 0, 0, 0, 0 2, 0, 0, 0, 0, 0, 2 2, 0, 0, 2, 0, 0, 2 2, 1, 1, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 2, 5 -------------------------------------------------- -------------------------------------------------- if Black moves in column, 2, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 2, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 2, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in column, 5 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 2, 0, 2, 0, 0, 2 2, 1, 0, 1, 1, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 3, 5 -------------------------------------------------- if Black moves in column, 3, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 2, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 2, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in columns 3, 6 We will only prove it for column, 3 Red can win in , 2, moves by putting its piece(1) in column, 3 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 1, 2, 0, 0, 2 2, 1, 2, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 4, 6 -------------------------------------------------- if Black moves in column, 4, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in columns 3, 5 We will only prove it for column, 3 Red can win in , 2, moves by putting its piece(1) in column, 3 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 2, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 1, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 2, 5 -------------------------------------------------- if Black moves in column, 5, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 2, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 1, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 2, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 1, moves by putting its piece(1) in column, 5 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 1, 0, 2 2, 1, 0, 1, 2, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red obviously won! -------------------------------------------------- if Black moves in column, 6, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 2, 2 from which Red can win in, 1, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 2, 2 Red can win in , 1, moves by putting its piece(1) in column, 6 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 1, 2 1, 1, 2, 2, 1, 2, 2 Red obviously won! -------------------------------------------------- if Black moves in column, 7, then the position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 from which Red can win in, 2, moves. Indeed -------------------------------- The position is 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 0, 0, 2, 0, 0, 2 2, 1, 0, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 Red can win in , 2, moves by putting its piece(1) in columns 3, 5 We will only prove it for column, 3 Red can win in , 2, moves by putting its piece(1) in column, 3 leading to position 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 2 2, 0, 0, 2, 0, 0, 2 2, 1, 1, 1, 0, 0, 1 1, 2, 1, 1, 1, 0, 2 1, 1, 2, 2, 1, 0, 2 This is a double-or-nothing in columns, 2, 5 --------------------------------------------------