上面的程序中由于一个BUG,没有用到除法,所以多了5种不可能。
True (1, 2, 3, 4): ( ( (4 * 2) * 3) * 1)
True (1, 2, 3, 5): ( ( (3 + 2) * 5) - 1)
True (1, 2, 3, 6): ( ( (6 + 2) * 3) * 1)
True (1, 2, 3, 7): ( ( (7 * 3) + 2) + 1)
True (1, 2, 3, 8): ( (8 + (1 + 3) ) * 2)
True (1, 2, 3, 9): ( ( (9 * 3) - 2) - 1)
True (1, 2, 4, 5): ( ( (5 + 2) - 1) * 4)
True (1, 2, 4, 6): ( (6 * (2 - 1) ) * 4)
True (1, 2, 4, 7): ( (7 + (1 + 4) ) * 2)
True (1, 2, 4, 8): ( ( (8 - 2) * 4) * 1)
True (1, 2, 4, 9): ( (9 + (4 - 1) ) * 2)
True (1, 2, 5, 6): ( ( (1 + 5) + 6) * 2)
True (1, 2, 5, 7): ( ( (7 - 2) * 5) - 1)
True (1, 2, 5, 8): ( (8 * (5 - 2) ) * 1)
True (1, 2, 5, 9): ( ( (9 * 2) + 5) + 1)
True (1, 2, 6, 7): ( (7 + (6 - 1) ) * 2)
True (1, 2, 6, 8): ( (6 * (8 / 2) ) * 1)
True (1, 2, 6, 9): ( ( (9 * 2) + 6) * 1)
True (1, 2, 7, 8): ( ( (8 * 2) + 7) + 1)
True (1, 2, 7, 9): ( ( (7 * 2) + 9) + 1)
True (1, 2, 8, 9): ( ( (8 * 2) + 9) - 1)
True (1, 3, 4, 5): ( ( (5 * 4) + 3) + 1)
False (1, 3, 4, 6): can not build operations
True (1, 3, 4, 7): ( ( (7 * 3) + 4) - 1)
True (1, 3, 4, 8): ( ( (8 - 3) + 1) * 4)
True (1, 3, 4, 9): ( ( (9 * 3) - 4) + 1)
True (1, 3, 5, 6): ( ( (6 * 3) + 5) + 1)
True (1, 3, 5, 7): ( (3 - 1) * (5 + 7) )
True (1, 3, 5, 8): ( ( (5 * 3) + 8) + 1)
True (1, 3, 5, 9): ( ( (5 * 3) + 9) * 1)
True (1, 3, 6, 7): ( ( (6 * 3) + 7) - 1)
True (1, 3, 6, 8): ( (8 * (6 - 3) ) * 1)
True (1, 3, 6, 9): ( (9 * (3 - 1) ) + 6)
True (1, 3, 7, 8): (8 * ( (7 - 3) - 1) )
True (1, 3, 7, 9): ( (9 * (1 + 7) ) / 3)
True (1, 3, 8, 9): ( (8 * (9 / 3) ) * 1)
False (1, 4, 5, 6): can not build operations
True (1, 4, 5, 7): ( ( (7 * 4) - 5) + 1)
True (1, 4, 5, 8): ( ( (5 - 1) * 4) + 8)
True (1, 4, 5, 9): ( ( (9 - 4) * 5) - 1)
True (1, 4, 6, 7): (6 * ( (7 - 4) + 1) )
True (1, 4, 6, 8): ( (6 * (8 - 4) ) * 1)
True (1, 4, 6, 9): (6 * ( (9 - 4) - 1) )
True (1, 4, 7, 8): ( ( (8 * 4) - 7) - 1)
True (1, 4, 7, 9): ( (7 - 4) * (9 - 1) )
True (1, 4, 8, 9): ( ( (8 * 4) - 9) + 1)
True (1, 5, 6, 7): ( ( (6 * 5) - 7) + 1)
True (1, 5, 6, 8): (6 * ( (8 - 5) + 1) )
True (1, 5, 6, 9): ( (6 * (9 - 5) ) * 1)
True (1, 5, 7, 8): (8 * ( (7 - 5) + 1) )
True (1, 5, 7, 9): ( (7 - 1) * (9 - 5) )
True (1, 5, 8, 9): (8 * ( (9 - 5) - 1) )
False (1, 6, 7, 8): can not build operations
True (1, 6, 7, 9): ( (1 + 7) * (9 - 6) )
True (1, 6, 8, 9): ( ( (9 + 6) + 8) + 1)
True (1, 7, 8, 9): ( ( (9 + 7) + 8) * 1)
True (2, 3, 4, 5): ( ( (5 + 3) + 4) * 2)
True (2, 3, 4, 6): ( ( (6 * 3) + 4) + 2)
True (2, 3, 4, 7): ( ( (7 + 3) * 2) + 4)
True (2, 3, 4, 8): ( ( (8 - 4) * 3) * 2)
True (2, 3, 4, 9): ( (4 * (9 / 3) ) * 2)
True (2, 3, 5, 6): ( (6 * (5 - 3) ) * 2)
True (2, 3, 5, 7): ( ( (5 * 3) + 7) + 2)
True (2, 3, 5, 8): ( ( (2 * 8) + 5) + 3)
True (2, 3, 5, 9): ( ( (9 * 3) - 5) + 2)
True (2, 3, 6, 7): ( (7 * (6 / 2) ) + 3)
True (2, 3, 6, 8): ( ( (6 * 3) + 8) - 2)
True (2, 3, 6, 9): ( ( (9 - 3) + 6) * 2)
True (2, 3, 7, 8): ( (7 + (8 - 3) ) * 2)
True (2, 3, 7, 9): ( ( (7 * 3) - 9) * 2)
True (2, 3, 8, 9): ( (8 * (9 - 3) ) / 2)
True (2, 4, 5, 6): ( ( (6 * 5) - 4) - 2)
True (2, 4, 5, 7): ( ( (7 + 5) * 4) / 2)
True (2, 4, 5, 8): ( (4 * (8 - 5) ) * 2)
True (2, 4, 5, 9): ( ( (9 + 5) * 2) - 4)
True (2, 4, 6, 7): ( ( (7 * 4) - 6) + 2)
True (2, 4, 6, 8): ( ( (8 * 4) - 6) - 2)
True (2, 4, 6, 9): ( (4 * (9 - 6) ) * 2)
True (2, 4, 7, 8): ( (7 * (8 / 2) ) - 4)
True (2, 4, 7, 9): ( (7 + (9 - 4) ) * 2)
True (2, 4, 8, 9): (8 * ( (9 - 4) - 2) )
True (2, 5, 6, 7): ( (6 * (7 - 5) ) * 2)
True (2, 5, 6, 8): ( ( (6 * 5) - 8) + 2)
True (2, 5, 6, 9): ( ( (6 * 5) / 2) + 9)
True (2, 5, 7, 8): (8 * ( (2 * 5) - 7) )
True (2, 5, 7, 9): ( ( (7 * 5) - 9) - 2)
True (2, 5, 8, 9): ( ( (9 + 5) + 8) + 2)
True (2, 6, 7, 8): ( ( (8 + 7) * 2) - 6)
True (2, 6, 7, 9): ( ( (9 + 6) + 7) + 2)
True (2, 6, 8, 9): ( ( (9 * 8) / 6) * 2)
True (2, 7, 8, 9): ( ( (9 + 7) * 2) - 8)
True (3, 4, 5, 6): (6 * (3 + (5 - 4) ) )
True (3, 4, 5, 7): ( ( (5 * 4) + 7) - 3)
True (3, 4, 5, 8): ( ( (8 * 4) - 5) - 3)
True (3, 4, 5, 9): ( ( (9 + 4) - 5) * 3)
False (3, 4, 6, 7): can not build operations
True (3, 4, 6, 8): ( (6 + (8 / 4) ) * 3)
True (3, 4, 6, 9): ( (9 - (6 - 3) ) * 4)
True (3, 4, 7, 8): ( ( (7 - 3) * 4) + 8)
True (3, 4, 7, 9): ( (9 * (7 - 4) ) - 3)
True (3, 4, 8, 9): ( ( (9 + 4) + 8) + 3)
True (3, 5, 6, 7): ( (6 + (7 - 5) ) * 3)
True (3, 5, 6, 8): ( (8 * (6 - 5) ) * 3)
True (3, 5, 6, 9): ( ( (6 * 5) - 9) + 3)
True (3, 5, 7, 8): ( (7 * (8 - 5) ) + 3)
True (3, 5, 7, 9): ( ( (9 + 5) + 7) + 3)
True (3, 5, 8, 9): ( (9 * (8 - 5) ) - 3)
True (3, 6, 7, 8): ( ( (8 + 6) + 7) + 3)
True (3, 6, 7, 9): ( (7 * (9 - 6) ) + 3)
True (3, 6, 8, 9): (6 * (9 - (8 - 3) ) )
True (3, 7, 8, 9): ( ( (9 + 7) - 8) * 3)
True (4, 5, 6, 7): ( ( (7 + 5) - 6) * 4)
True (4, 5, 6, 8): (8 * (4 - (6 - 5) ) )
True (4, 5, 6, 9): ( ( (9 + 5) + 6) + 4)
True (4, 5, 7, 8): ( ( (8 + 5) + 7) + 4)
True (4, 5, 7, 9): ( (7 * (9 - 5) ) - 4)
True (4, 5, 8, 9): ( ( (9 + 5) - 8) * 4)
True (4, 6, 7, 8): ( (6 * (8 - 7) ) * 4)
True (4, 6, 7, 9): ( ( (9 + 7) * 6) / 4)
True (4, 6, 8, 9): ( (6 * (9 - 8) ) * 4)
True (4, 7, 8, 9): ( (8 - (9 - 7) ) * 4)
True (5, 6, 7, 8): (6 * ( (5 + 7) - 8) )
True (5, 6, 7, 9): ( (9 * (7 - 5) ) + 6)
True (5, 6, 8, 9): ( ( (9 + 6) * 8) / 5)
True (5, 7, 8, 9): ( ( (5 * 8) - 9) - 7)
True (6, 7, 8, 9): (6 * (8 / (9 - 7) ) )