24点算不出结果的情况

时间: 2025-10-10 15:59:29

只用基本的交换位置，加减乘除和括号，不讨论其他运算符号以及高等数学里求导之类，只看原始规则

[1, 1, 1, 1] [1, 1, 1, 2] [1, 1, 1, 3] [1, 1, 1, 4] [1, 1, 1, 5] [1, 1, 1, 6] [1, 1, 1, 7] [1, 1, 1, 9] [1, 1, 1, 10] [1, 1, 2, 2] [1, 1, 2, 3] [1, 1, 2, 4] [1, 1, 2, 5] [1, 1, 3, 3] [1, 1, 4, 11] [1, 1, 5, 9] [1, 1, 5, 10] [1, 1, 5, 11] [1, 1, 5, 12] [1, 1, 6, 7] [1, 1, 6, 10] [1, 1, 6, 11] [1, 1, 7, 7] [1, 1, 7, 8] [1, 1, 7, 9] [1, 1, 7, 11] [1, 1, 7, 12] [1, 1, 8, 9] [1, 1, 8, 10] [1, 1, 8, 11] [1, 1, 8, 12] [1, 1, 9, 9] [1, 1, 9, 10] [1, 1, 9, 11] [1, 1, 9, 12] [1, 1, 10, 10] [1, 1, 10, 11] [1, 2, 2, 2] [1, 2, 2, 3] [1, 2, 5, 11] [1, 2, 8, 11] [1, 2, 8, 12] [1, 2, 9, 9] [1, 2, 9, 10] [1, 2, 10, 10] [1, 3, 5, 5] [1, 3, 7, 11] [1, 4, 7, 10] [1, 4, 8, 10] [1, 4, 9, 9] [1, 4, 11, 11] [1, 4, 11, 12] [1, 5, 5, 7] [1, 5, 5, 8] [1, 5, 7, 7] [1, 6, 6, 7] [1, 6, 7, 7] [1, 6, 7, 8] [1, 6, 9, 11] [1, 6, 10, 10] [1, 6, 10, 11] [1, 6, 11, 11] [1, 7, 7, 7] [1, 7, 7, 8] [1, 7, 10, 10] [1, 7, 10, 11] [1, 7, 11, 11] [1, 7, 11, 12] [1, 8, 9, 9] [1, 8, 9, 10] [1, 8, 10, 10] [1, 8, 11, 11] [1, 9, 9, 9] [1, 9, 9, 10] [1, 9, 9, 11] [1, 9, 10, 10] [1, 9, 10, 11] [1, 10, 10, 10] [1, 10, 10, 11] [1, 10, 11, 11] [1, 11, 11, 11] [2, 2, 2, 2] [2, 2, 2, 6] [2, 2, 7, 9] [2, 2, 7, 11] [2, 2, 8, 11] [2, 2, 9, 9] [2, 2, 10, 12] [2, 3, 3, 4] [2, 3, 9, 11] [2, 3, 10, 11] [2, 4, 9, 11] [2, 5, 5, 5] [2, 5, 5, 6] [2, 5, 7, 12] [2, 5, 9, 9] [2, 5, 11, 11] [2, 6, 7, 7] [2, 6, 11, 11] [2, 7, 7, 7] [2, 7, 7, 9] [2, 7, 8, 10] [2, 7, 9, 9] [2, 7, 9, 12] [2, 7, 11, 11] [2, 9, 9, 9] [2, 9, 9, 10] [2, 9, 11, 12] [2, 9, 12, 12] [2, 10, 10, 10] [2, 10, 12, 12] [3, 3, 4, 10] [3, 3, 5, 8] [3, 3, 5, 11] [3, 3, 7, 10] [3, 3, 8, 11] [3, 3, 10, 10] [3, 3, 10, 11] [3, 3, 10, 12] [3, 3, 11, 11] [3, 4, 6, 7] [3, 4, 8, 8] [3, 4, 9, 10] [3, 4, 10, 11] [3, 4, 11, 11] [3, 5, 5, 5] [3, 5, 5, 10] [3, 5, 7, 7] [3, 5, 8, 10] [3, 5, 9, 11] [3, 6, 7, 11] [3, 6, 8, 11] [3, 7, 7, 11] [3, 7, 8, 10] [3, 7, 10, 12] [3, 10, 10, 10] [3, 10, 10, 11] [3, 10, 11, 11] [3, 10, 12, 12] [3, 11, 11, 11] [4, 4, 5, 9] [4, 4, 6, 6] [4, 4, 6, 7] [4, 4, 7, 11] [4, 4, 9, 9] [4, 4, 9, 10] [4, 4, 10, 11] [4, 4, 11, 11] [4, 5, 5, 11] [4, 5, 5, 12] [4, 5, 9, 11] [4, 6, 6, 11] [4, 6, 7, 11] [4, 6, 8, 11] [4, 6, 9, 11] [4, 7, 7, 9] [4, 7, 7, 10] [4, 7, 7, 12] [4, 9, 9, 9] [4, 9, 9, 11] [4, 9, 10, 10] [4, 10, 10, 10] [4, 10, 11, 11] [4, 11, 11, 11] [4, 11, 11, 12] [4, 11, 12, 12] [5, 5, 5, 7] [5, 5, 5, 8] [5, 5, 5, 10] [5, 5, 5, 11] [5, 5, 6, 9] [5, 5, 6, 10] [5, 5, 6, 12] [5, 5, 7, 9] [5, 5, 7, 12] [5, 5, 9, 12] [5, 5, 10, 12] [5, 6, 6, 11] [5, 6, 7, 10] [5, 6, 7, 11] [5, 6, 8, 11] [5, 7, 7, 7] [5, 7, 7, 8] [5, 7, 7, 12] [5, 7, 8, 11] [5, 7, 8, 12] [5, 7, 9, 9] [5, 7, 11, 12] [5, 8, 8, 11] [5, 8, 8, 12] [5, 8, 9, 9] [5, 8, 9, 10] [5, 8, 10, 10] [5, 8, 11, 11] [5, 9, 9, 9] [5, 9, 9, 10] [5, 9, 10, 12] [5, 9, 11, 11] [5, 9, 11, 12] [5, 10, 10, 10] [5, 10, 11, 12] [5, 10, 12, 12] [5, 11, 11, 11] [5, 11, 11, 12] [5, 12, 12, 12] [6, 6, 6, 7] [6, 6, 7, 7] [6, 6, 7, 8] [6, 6, 9, 9] [6, 6, 10, 10] [6, 6, 10, 11] [6, 6, 11, 11] [6, 7, 7, 7] [6, 7, 7, 8] [6, 7, 7, 9] [6, 7, 7, 12] [6, 7, 8, 8] [6, 7, 9, 10] [6, 7, 9, 11] [6, 7, 10, 11] [6, 8, 10, 10] [6, 9, 9, 9] [6, 9, 10, 10] [6, 9, 11, 11] [6, 10, 10, 11] [6, 10, 10, 12] [6, 10, 11, 11] [6, 11, 11, 11] [7, 7, 7, 7] [7, 7, 7, 8] [7, 7, 7, 9] [7, 7, 7, 10] [7, 7, 7, 11] [7, 7, 8, 8] [7, 7, 8, 9] [7, 7, 8, 10] [7, 7, 8, 12] [7, 7, 9, 9] [7, 7, 9, 11] [7, 7, 9, 12] [7, 7, 10, 10] [7, 7, 10, 11] [7, 7, 10, 12] [7, 7, 11, 11] [7, 8, 8, 8] [7, 8, 9, 9] [7, 8, 9, 11] [7, 8, 10, 12] [7, 8, 11, 11] [7, 9, 9, 9] [7, 9, 9, 10] [7, 9, 9, 11] [7, 9, 9, 12] [7, 9, 10, 10] [7, 10, 10, 10] [7, 10, 11, 11] [7, 10, 11, 12] [7, 11, 11, 11] [7, 11, 11, 12] [7, 11, 12, 12] [7, 12, 12, 12] [8, 8, 8, 8] [8, 8, 8, 9] [8, 8, 9, 9] [8, 8, 9, 10] [8, 8, 10, 10] [8, 8, 10, 11] [8, 8, 11, 11] [8, 9, 9, 9] [8, 9, 9, 10] [8, 9, 9, 11] [8, 9, 10, 10] [8, 9, 10, 11] [8, 10, 10, 10] [8, 10, 10, 11] [8, 10, 11, 12] [8, 11, 11, 11] [8, 11, 11, 12] [8, 12, 12, 12] [9, 9, 9, 9] [9, 9, 9, 10] [9, 9, 9, 11] [9, 9, 10, 10] [9, 9, 10, 11] [9, 9, 10, 12] [9, 9, 11, 11] [9, 10, 10, 10] [9, 10, 10, 11] [9, 10, 10, 12] [9, 10, 11, 11] [9, 11, 11, 12] [10, 10, 10, 10] [10, 10, 10, 11] [10, 10, 11, 11] [10, 11, 11, 11] [11, 11, 11, 11]