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