24点游戏 有解的组合

1，2，3，4

2，3，4，5

3，4，5，6

6，7，8，9

7，8，9，10

8，9，10，11  无解

9，10，11，12

10，11，12，13

 

13，5，8，9  5*9-13-8=24

 

总组合数（按数字，忽略花色）：1820

确答案 1820 是可重复组合数，计算过程是这样的：

• 第一步：转化为“插板法”问题
  我们要从13个数字（1到13）里，允许重复地选出4个，并且不考虑顺序。这相当于把4个“球”（牌的位置）放进13个“盒子”（数字1到13）里，每个盒子可以放多个球。

• 第二步：代入组合公式
  可重复组合的公式是：C(总数 + 个数 - 1, 个数)
  在这里，总数是13（数字种类），个数是4（要抽的牌数）：
  C(13 + 4 - 1, 4) = C(16, 4)

• 第三步：计算结果
  C(16, 4) = (16 × 15 × 14 × 13) ÷ (4 × 3 × 2 × 1) = 43680 ÷ 24 = 1820

 

1, 1, 1, 8    (1+1+1)*8=24
1, 1, 1, 11  (1+1)*(1+11)=24
1, 1, 1, 12  (1+1)*1*12=24
1, 1, 1, 13  (1+1)*(13-1)=24
1, 1, 2, 6
1, 1, 2, 7
1, 1, 2, 8
1, 1, 2, 9
1, 1, 2, 10
1, 1, 2, 11
1, 1, 2, 12
1, 1, 2, 13
1, 1, 3, 4
1, 1, 3, 5
1, 1, 3, 6
1, 1, 3, 7
1, 1, 3, 8
1, 1, 3, 9
1, 1, 3, 10
1, 1, 3, 11
1, 1, 3, 12
1, 1, 3, 13
1, 1, 4, 4
1, 1, 4, 5
1, 1, 4, 6
1, 1, 4, 7
1, 1, 4, 8
1, 1, 4, 9
1, 1, 4, 10
1, 1, 4, 12
1, 1, 5, 5
1, 1, 5, 6
1, 1, 5, 7
1, 1, 5, 8
1, 1, 6, 6
1, 1, 6, 8
1, 1, 6, 9
1, 1, 6, 12
1, 1, 7, 10
1, 1, 8, 8
1, 1, 9, 13
1, 1, 10, 12
1, 1, 10, 13
1, 1, 11, 11
1, 1, 11, 12
1, 1, 11, 13
1, 1, 12, 12
1, 1, 12, 13
1, 1, 13, 13
1, 2, 2, 4
1, 2, 2, 5
1, 2, 2, 6
1, 2, 2, 7
1, 2, 2, 8
1, 2, 2, 9
1, 2, 2, 10
1, 2, 2, 11
1, 2, 2, 12
1, 2, 2, 13
1, 2, 3, 3
1, 2, 3, 4
1, 2, 3, 5
1, 2, 3, 6
1, 2, 3, 7
1, 2, 3, 8
1, 2, 3, 9
1, 2, 3, 10
1, 2, 3, 11
1, 2, 3, 12
1, 2, 3, 13
1, 2, 4, 4
1, 2, 4, 5
1, 2, 4, 6
1, 2, 4, 7
1, 2, 4, 8
1, 2, 4, 9
1, 2, 4, 10
1, 2, 4, 11
1, 2, 4, 12
1, 2, 4, 13
1, 2, 5, 5
1, 2, 5, 6
1, 2, 5, 7
1, 2, 5, 8
1, 2, 5, 9
1, 2, 5, 10
1, 2, 5, 12
1, 2, 5, 13
1, 2, 6, 6
1, 2, 6, 7
1, 2, 6, 8
1, 2, 6, 9
1, 2, 6, 10
1, 2, 6, 11
1, 2, 6, 12
1, 2, 6, 13
1, 2, 7, 7
1, 2, 7, 8
1, 2, 7, 9
1, 2, 7, 10
1, 2, 7, 11
1, 2, 7, 12
1, 2, 8, 8
1, 2, 8, 9
1, 2, 8, 10
1, 2, 8, 13
1, 2, 9, 11
1, 2, 9, 12
1, 2, 9, 13
1, 2, 10, 11
1, 2, 10, 12
1, 2, 10, 13
1, 2, 11, 11
1, 2, 11, 12
1, 2, 11, 13
1, 2, 12, 12
1, 2, 12, 13
1, 2, 13, 13
1, 3, 3, 3
1, 3, 3, 4
1, 3, 3, 5
1, 3, 3, 6
1, 3, 3, 7
1, 3, 3, 8
1, 3, 3, 9
1, 3, 3, 10
1, 3, 3, 11
1, 3, 3, 12
1, 3, 4, 4
1, 3, 4, 5
1, 3, 4, 6
1, 3, 4, 7
1, 3, 4, 8
1, 3, 4, 9
1, 3, 4, 10
1, 3, 4, 11
1, 3, 4, 12
1, 3, 4, 13
1, 3, 5, 6
1, 3, 5, 7
1, 3, 5, 8
1, 3, 5, 9
1, 3, 5, 10
1, 3, 5, 11
1, 3, 5, 12
1, 3, 5, 13
1, 3, 6, 6
1, 3, 6, 7
1, 3, 6, 8
1, 3, 6, 9
1, 3, 6, 10
1, 3, 6, 11
1, 3, 6, 12
1, 3, 6, 13
1, 3, 7, 7
1, 3, 7, 8
1, 3, 7, 9
1, 3, 7, 10
1, 3, 7, 12
1, 3, 7, 13
1, 3, 8, 8
1, 3, 8, 9
1, 3, 8, 10
1, 3, 8, 11
1, 3, 8, 12
1, 3, 8, 13
1, 3, 9, 9
1, 3, 9, 10
1, 3, 9, 11
1, 3, 9, 12
1, 3, 9, 13
1, 3, 10, 10
1, 3, 10, 11
1, 3, 10, 12
1, 3, 11, 11
1, 3, 11, 12
1, 3, 12, 12
1, 3, 12, 13
1, 3, 13, 13
1, 4, 4, 4
1, 4, 4, 5
1, 4, 4, 6
1, 4, 4, 7
1, 4, 4, 8
1, 4, 4, 9
1, 4, 4, 10
1, 4, 4, 11
1, 4, 4, 12
1, 4, 5, 5
1, 4, 5, 6
1, 4, 5, 7
1, 4, 5, 8
1, 4, 5, 9
1, 4, 5, 10
1, 4, 5, 11
1, 4, 5, 12
1, 4, 5, 13
1, 4, 6, 6
1, 4, 6, 7
1, 4, 6, 8
1, 4, 6, 9
1, 4, 6, 10
1, 4, 6, 11
1, 4, 6, 12
1, 4, 6, 13
1, 4, 7, 7
1, 4, 7, 8
1, 4, 7, 9
1, 4, 7, 11
1, 4, 7, 12
1, 4, 7, 13
1, 4, 8, 8
1, 4, 8, 9
1, 4, 8, 11
1, 4, 8, 12
1, 4, 8, 13
1, 4, 9, 10
1, 4, 9, 11
1, 4, 9, 12
1, 4, 9, 13
1, 4, 10, 10
1, 4, 10, 11
1, 4, 10, 12
1, 4, 12, 12
1, 5, 5, 5
1, 5, 5, 6
1, 5, 5, 9
1, 5, 5, 10
1, 5, 5, 11
1, 5, 5, 12
1, 5, 5, 13
1, 5, 6, 6
1, 5, 6, 7
1, 5, 6, 8
1, 5, 6, 9
1, 5, 6, 10
1, 5, 6, 11
1, 5, 6, 12
1, 5, 6, 13
1, 5, 7, 8
1, 5, 7, 9
1, 5, 7, 10
1, 5, 7, 11
1, 5, 7, 12
1, 5, 7, 13
1, 5, 8, 8
1, 5, 8, 9
1, 5, 8, 10
1, 5, 8, 11
1, 5, 8, 12
1, 5, 8, 13
1, 5, 9, 9
1, 5, 9, 10
1, 5, 9, 11
1, 5, 9, 12
1, 5, 9, 13
1, 5, 10, 10
1, 5, 10, 11
1, 5, 10, 12
1, 5, 10, 13
1, 5, 11, 11
1, 5, 11, 12
1, 5, 12, 12
1, 6, 6, 6
1, 6, 6, 8
1, 6, 6, 9
1, 6, 6, 10
1, 6, 6, 11
1, 6, 6, 12
1, 6, 6, 13
1, 6, 7, 9
1, 6, 7, 10
1, 6, 7, 11
1, 6, 7, 12
1, 6, 8, 8
1, 6, 8, 9
1, 6, 8, 10
1, 6, 8, 11
1, 6, 8, 12
1, 6, 8, 13
1, 6, 9, 9
1, 6, 9, 10
1, 6, 9, 12
1, 6, 9, 13
1, 6, 10, 12
1, 6, 10, 13
1, 6, 11, 12
1, 6, 11, 13
1, 6, 12, 12
1, 6, 12, 13
1, 7, 7, 9
1, 7, 7, 10
1, 7, 7, 11
1, 7, 7, 12
1, 7, 8, 8
1, 7, 8, 9
1, 7, 8, 10
1, 7, 8, 11
1, 7, 8, 12
1, 7, 9, 9
1, 7, 9, 10
1, 7, 9, 11
1, 7, 9, 12
1, 7, 9, 13
1, 7, 10, 12
1, 7, 10, 13
1, 7, 12, 12
1, 7, 12, 13
1, 7, 13, 13
1, 8, 8, 8
1, 8, 8, 9
1, 8, 8, 10
1, 8, 8, 11
1, 8, 8, 12
1, 8, 9, 11
1, 8, 9, 12
1, 8, 9, 13
1, 8, 10, 11
1, 8, 10, 12
1, 8, 10, 13
1, 8, 11, 12
1, 8, 11, 13
1, 8, 12, 12
1, 9, 9, 12
1, 9, 10, 12
1, 9, 10, 13
1, 9, 11, 11
1, 9, 11, 12
1, 9, 11, 13
1, 9, 12, 12
1, 10, 10, 12
1, 10, 11, 12
1, 10, 12, 12
1, 10, 12, 13
1, 11, 11, 12
1, 11, 11, 13
1, 11, 12, 12
1, 11, 12, 13
1, 11, 13, 13
1, 12, 12, 12
1, 12, 12, 13
1, 12, 13, 13
2, 2, 2, 3
2, 2, 2, 4
2, 2, 2, 5
2, 2, 2, 7
2, 2, 2, 8
2, 2, 2, 9
2, 2, 2, 10
2, 2, 2, 11
2, 2, 2, 12
2, 2, 2, 13
2, 2, 3, 3
2, 2, 3, 4
2, 2, 3, 5
2, 2, 3, 6
2, 2, 3, 7
2, 2, 3, 8
2, 2, 3, 9
2, 2, 3, 10
2, 2, 3, 11
2, 2, 3, 12
2, 2, 3, 13
2, 2, 4, 4
2, 2, 4, 5
2, 2, 4, 6
2, 2, 4, 7
2, 2, 4, 8
2, 2, 4, 9
2, 2, 4, 10
2, 2, 4, 11
2, 2, 4, 12
2, 2, 4, 13
2, 2, 5, 5
2, 2, 5, 6
2, 2, 5, 7
2, 2, 5, 8
2, 2, 5, 9
2, 2, 5, 10
2, 2, 5, 11
2, 2, 5, 12
2, 2, 6, 6
2, 2, 6, 7
2, 2, 6, 8
2, 2, 6, 9
2, 2, 6, 10
2, 2, 6, 11
2, 2, 6, 12
2, 2, 6, 13
2, 2, 7, 7
2, 2, 7, 8
2, 2, 7, 10
2, 2, 7, 12
2, 2, 7, 13
2, 2, 8, 8
2, 2, 8, 9
2, 2, 8, 10
2, 2, 8, 12
2, 2, 9, 10
2, 2, 9, 11
2, 2, 9, 12
2, 2, 10, 10
2, 2, 10, 11
2, 2, 10, 13
2, 2, 11, 11
2, 2, 11, 12
2, 2, 11, 13
2, 2, 12, 12
2, 2, 12, 13
2, 2, 13, 13
2, 3, 3, 3
2, 3, 3, 5
2, 3, 3, 6
2, 3, 3, 7
2, 3, 3, 8
2, 3, 3, 9
2, 3, 3, 10
2, 3, 3, 11
2, 3, 3, 12
2, 3, 3, 13
2, 3, 4, 4
2, 3, 4, 5
2, 3, 4, 6
2, 3, 4, 7
2, 3, 4, 8
2, 3, 4, 9
2, 3, 4, 10
2, 3, 4, 11
2, 3, 4, 12
2, 3, 4, 13
2, 3, 5, 5
2, 3, 5, 6
2, 3, 5, 7
2, 3, 5, 8
2, 3, 5, 9
2, 3, 5, 10
2, 3, 5, 11
2, 3, 5, 12
2, 3, 5, 13
2, 3, 6, 6
2, 3, 6, 7
2, 3, 6, 8
2, 3, 6, 9
2, 3, 6, 10
2, 3, 6, 11
2, 3, 6, 12
2, 3, 6, 13
2, 3, 7, 7
2, 3, 7, 8
2, 3, 7, 9
2, 3, 7, 10
2, 3, 7, 11
2, 3, 7, 12
2, 3, 7, 13
2, 3, 8, 8
2, 3, 8, 9
2, 3, 8, 10
2, 3, 8, 11
2, 3, 8, 12
2, 3, 8, 13
2, 3, 9, 9
2, 3, 9, 10
2, 3, 9, 12
2, 3, 9, 13
2, 3, 10, 10
2, 3, 10, 12
2, 3, 10, 13
2, 3, 11, 11
2, 3, 11, 12
2, 3, 11, 13
2, 3, 12, 12
2, 3, 12, 13
2, 3, 13, 13
2, 4, 4, 4
2, 4, 4, 5
2, 4, 4, 6
2, 4, 4, 7
2, 4, 4, 8
2, 4, 4, 9
2, 4, 4, 10
2, 4, 4, 11
2, 4, 4, 12
2, 4, 4, 13
2, 4, 5, 5
2, 4, 5, 6
2, 4, 5, 7
2, 4, 5, 8
2, 4, 5, 9
2, 4, 5, 10
2, 4, 5, 11
2, 4, 5, 12
2, 4, 5, 13
2, 4, 6, 6
2, 4, 6, 7
2, 4, 6, 8
2, 4, 6, 9
2, 4, 6, 10
2, 4, 6, 11
2, 4, 6, 12
2, 4, 6, 13
2, 4, 7, 7
2, 4, 7, 8
2, 4, 7, 9
2, 4, 7, 10
2, 4, 7, 11
2, 4, 7, 12
2, 4, 8, 8
2, 4, 8, 9
2, 4, 8, 10
2, 4, 8, 11
2, 4, 8, 12
2, 4, 8, 13
2, 4, 9, 9
2, 4, 9, 10
2, 4, 9, 12
2, 4, 9, 13
2, 4, 10, 10
2, 4, 10, 11
2, 4, 10, 12
2, 4, 10, 13
2, 4, 11, 11
2, 4, 11, 12
2, 4, 12, 12
2, 4, 13, 13
2, 5, 5, 7
2, 5, 5, 8
2, 5, 5, 9
2, 5, 5, 10
2, 5, 5, 11
2, 5, 5, 12
2, 5, 5, 13
2, 5, 6, 6
2, 5, 6, 7
2, 5, 6, 8
2, 5, 6, 9
2, 5, 6, 10
2, 5, 6, 11
2, 5, 6, 12
2, 5, 6, 13
2, 5, 7, 7
2, 5, 7, 8
2, 5, 7, 9
2, 5, 7, 10
2, 5, 7, 11
2, 5, 7, 13
2, 5, 8, 8
2, 5, 8, 9
2, 5, 8, 10
2, 5, 8, 11
2, 5, 8, 12
2, 5, 8, 13
2, 5, 9, 10
2, 5, 9, 11
2, 5, 9, 12
2, 5, 10, 10
2, 5, 10, 11
2, 5, 10, 12
2, 5, 10, 13
2, 5, 11, 12
2, 5, 12, 12
2, 5, 12, 13
2, 6, 6, 6
2, 6, 6, 7
2, 6, 6, 8
2, 6, 6, 9
2, 6, 6, 10
2, 6, 6, 11
2, 6, 6, 12
2, 6, 6, 13
2, 6, 7, 8
2, 6, 7, 9
2, 6, 7, 10
2, 6, 7, 11
2, 6, 7, 12
2, 6, 7, 13
2, 6, 8, 8
2, 6, 8, 9
2, 6, 8, 10
2, 6, 8, 11
2, 6, 8, 12
2, 6, 8, 13
2, 6, 9, 9
2, 6, 9, 10
2, 6, 9, 11
2, 6, 9, 12
2, 6, 10, 10
2, 6, 10, 11
2, 6, 10, 12
2, 6, 10, 13
2, 6, 11, 12
2, 6, 11, 13
2, 6, 12, 12
2, 6, 12, 13
2, 7, 7, 8
2, 7, 7, 10
2, 7, 7, 11
2, 7, 7, 12
2, 7, 7, 13
2, 7, 8, 8
2, 7, 8, 9
2, 7, 8, 11
2, 7, 8, 12
2, 7, 8, 13
2, 7, 9, 10
2, 7, 9, 11
2, 7, 9, 13
2, 7, 10, 10
2, 7, 10, 11
2, 7, 10, 12
2, 7, 11, 12
2, 7, 12, 12
2, 7, 12, 13
2, 8, 8, 8
2, 8, 8, 9
2, 8, 8, 10
2, 8, 8, 11
2, 8, 8, 12
2, 8, 8, 13
2, 8, 9, 9
2, 8, 9, 10
2, 8, 9, 11
2, 8, 9, 12
2, 8, 9, 13
2, 8, 10, 10
2, 8, 10, 11
2, 8, 10, 12
2, 8, 10, 13
2, 8, 11, 11
2, 8, 11, 12
2, 8, 12, 12
2, 8, 12, 13
2, 8, 13, 13
2, 9, 9, 11
2, 9, 9, 12
2, 9, 9, 13
2, 9, 10, 10
2, 9, 10, 11
2, 9, 10, 12
2, 9, 10, 13
2, 9, 11, 11
2, 9, 11, 13
2, 9, 12, 13
2, 9, 13, 13
2, 10, 10, 11
2, 10, 10, 12
2, 10, 10, 13
2, 10, 11, 11
2, 10, 11, 12
2, 10, 11, 13
2, 10, 12, 13
2, 11, 11, 11
2, 11, 11, 12
2, 11, 11, 13
2, 11, 12, 12
2, 11, 12, 13
2, 11, 13, 13
2, 12, 12, 12
2, 12, 12, 13
2, 12, 13, 13
2, 13, 13, 13
3, 3, 3, 3
3, 3, 3, 4
3, 3, 3, 5
3, 3, 3, 6
3, 3, 3, 7
3, 3, 3, 8
3, 3, 3, 9
3, 3, 3, 10
3, 3, 3, 11
3, 3, 3, 12
3, 3, 4, 4
3, 3, 4, 5
3, 3, 4, 6
3, 3, 4, 7
3, 3, 4, 8
3, 3, 4, 9
3, 3, 4, 11
3, 3, 4, 12
3, 3, 4, 13
3, 3, 5, 5
3, 3, 5, 6
3, 3, 5, 7
3, 3, 5, 9
3, 3, 5, 10
3, 3, 5, 12
3, 3, 5, 13
3, 3, 6, 6
3, 3, 6, 7
3, 3, 6, 8
3, 3, 6, 9
3, 3, 6, 10
3, 3, 6, 11
3, 3, 6, 12
3, 3, 6, 13
3, 3, 7, 7
3, 3, 7, 8
3, 3, 7, 9
3, 3, 7, 11
3, 3, 7, 12
3, 3, 7, 13
3, 3, 8, 8
3, 3, 8, 9
3, 3, 8, 10
3, 3, 8, 12
3, 3, 8, 13
3, 3, 9, 9
3, 3, 9, 10
3, 3, 9, 11
3, 3, 9, 12
3, 3, 9, 13
3, 3, 10, 13
3, 3, 11, 12
3, 3, 11, 13
3, 3, 12, 12
3, 3, 12, 13
3, 4, 4, 4
3, 4, 4, 5
3, 4, 4, 6
3, 4, 4, 7
3, 4, 4, 8
3, 4, 4, 9
3, 4, 4, 10
3, 4, 4, 11
3, 4, 4, 12
3, 4, 4, 13
3, 4, 5, 5
3, 4, 5, 6
3, 4, 5, 7
3, 4, 5, 8
3, 4, 5, 9
3, 4, 5, 10
3, 4, 5, 11
3, 4, 5, 12
3, 4, 5, 13
3, 4, 6, 6
3, 4, 6, 8
3, 4, 6, 9
3, 4, 6, 10
3, 4, 6, 11
3, 4, 6, 12
3, 4, 6, 13
3, 4, 7, 7
3, 4, 7, 8
3, 4, 7, 9
3, 4, 7, 10
3, 4, 7, 11
3, 4, 7, 12
3, 4, 8, 9
3, 4, 8, 10
3, 4, 8, 11
3, 4, 8, 12
3, 4, 8, 13
3, 4, 9, 9
3, 4, 9, 11
3, 4, 9, 12
3, 4, 9, 13
3, 4, 10, 10
3, 4, 10, 12
3, 4, 10, 13
3, 4, 11, 12
3, 4, 11, 13
3, 4, 12, 12
3, 4, 12, 13
3, 5, 5, 6
3, 5, 5, 7
3, 5, 5, 8
3, 5, 5, 9
3, 5, 5, 11
3, 5, 5, 12
3, 5, 6, 6
3, 5, 6, 7
3, 5, 6, 8
3, 5, 6, 9
3, 5, 6, 10
3, 5, 6, 11
3, 5, 6, 12
3, 5, 6, 13
3, 5, 7, 8
3, 5, 7, 9
3, 5, 7, 10
3, 5, 7, 11
3, 5, 7, 12
3, 5, 7, 13
3, 5, 8, 8
3, 5, 8, 9
3, 5, 8, 11
3, 5, 8, 12
3, 5, 8, 13
3, 5, 9, 9
3, 5, 9, 10
3, 5, 9, 12
3, 5, 9, 13
3, 5, 10, 10
3, 5, 10, 11
3, 5, 10, 12
3, 5, 10, 13
3, 5, 11, 11
3, 5, 11, 12
3, 5, 12, 12
3, 5, 12, 13
3, 5, 13, 13
3, 6, 6, 6
3, 6, 6, 7
3, 6, 6, 8
3, 6, 6, 9
3, 6, 6, 10
3, 6, 6, 11
3, 6, 6, 12
3, 6, 6, 13
3, 6, 7, 7
3, 6, 7, 8
3, 6, 7, 9
3, 6, 7, 10
3, 6, 7, 12
3, 6, 7, 13
3, 6, 8, 8
3, 6, 8, 9
3, 6, 8, 10
3, 6, 8, 12
3, 6, 8, 13
3, 6, 9, 9
3, 6, 9, 10
3, 6, 9, 11
3, 6, 9, 12
3, 6, 9, 13
3, 6, 10, 10
3, 6, 10, 11
3, 6, 10, 12
3, 6, 11, 11
3, 6, 11, 12
3, 6, 11, 13
3, 6, 12, 12
3, 6, 12, 13
3, 6, 13, 13
3, 7, 7, 7
3, 7, 7, 8
3, 7, 7, 9
3, 7, 7, 10
3, 7, 7, 12
3, 7, 7, 13
3, 7, 8, 8
3, 7, 8, 9
3, 7, 8, 11
3, 7, 8, 12
3, 7, 8, 13
3, 7, 9, 9
3, 7, 9, 10
3, 7, 9, 11
3, 7, 9, 12
3, 7, 9, 13
3, 7, 10, 10
3, 7, 10, 11
3, 7, 10, 13
3, 7, 11, 11
3, 7, 11, 12
3, 7, 12, 12
3, 7, 12, 13
3, 7, 13, 13
3, 8, 8, 8
3, 8, 8, 9
3, 8, 8, 10
3, 8, 8, 11
3, 8, 8, 12
3, 8, 9, 9
3, 8, 9, 10
3, 8, 9, 11
3, 8, 9, 12
3, 8, 9, 13
3, 8, 10, 10
3, 8, 10, 11
3, 8, 10, 12
3, 8, 11, 11
3, 8, 11, 12
3, 8, 12, 12
3, 8, 12, 13
3, 8, 13, 13
3, 9, 9, 9
3, 9, 9, 10
3, 9, 9, 11
3, 9, 9, 12
3, 9, 9, 13
3, 9, 10, 10
3, 9, 10, 11
3, 9, 10, 12
3, 9, 10, 13
3, 9, 11, 11
3, 9, 11, 12
3, 9, 11, 13
3, 9, 12, 12
3, 9, 12, 13
3, 9, 13, 13
3, 10, 10, 12
3, 10, 11, 12
3, 10, 11, 13
3, 11, 11, 12
3, 11, 12, 12
3, 12, 12, 12
3, 12, 12, 13
3, 12, 13, 13
4, 4, 4, 4
4, 4, 4, 5
4, 4, 4, 6
4, 4, 4, 7
4, 4, 4, 8
4, 4, 4, 9
4, 4, 4, 10
4, 4, 4, 11
4, 4, 4, 12
4, 4, 5, 5
4, 4, 5, 6
4, 4, 5, 7
4, 4, 5, 8
4, 4, 5, 10
4, 4, 5, 11
4, 4, 5, 12
4, 4, 5, 13
4, 4, 6, 8
4, 4, 6, 9
4, 4, 6, 10
4, 4, 6, 11
4, 4, 6, 12
4, 4, 6, 13
4, 4, 7, 7
4, 4, 7, 8
4, 4, 7, 9
4, 4, 7, 10
4, 4, 7, 12
4, 4, 7, 13
4, 4, 8, 8
4, 4, 8, 9
4, 4, 8, 10
4, 4, 8, 11
4, 4, 8, 12
4, 4, 8, 13
4, 4, 9, 11
4, 4, 9, 12
4, 4, 10, 10
4, 4, 10, 12
4, 4, 10, 13
4, 4, 11, 12
4, 4, 11, 13
4, 4, 12, 12
4, 4, 12, 13
4, 5, 5, 5
4, 5, 5, 6
4, 5, 5, 7
4, 5, 5, 8
4, 5, 5, 9
4, 5, 5, 10
4, 5, 6, 6
4, 5, 6, 7
4, 5, 6, 8
4, 5, 6, 9
4, 5, 6, 10
4, 5, 6, 11
4, 5, 6, 12
4, 5, 6, 13
4, 5, 7, 7
4, 5, 7, 8
4, 5, 7, 9
4, 5, 7, 10
4, 5, 7, 11
4, 5, 7, 12
4, 5, 7, 13
4, 5, 8, 8
4, 5, 8, 9
4, 5, 8, 10
4, 5, 8, 11
4, 5, 8, 12
4, 5, 8, 13
4, 5, 9, 9
4, 5, 9, 10
4, 5, 9, 12
4, 5, 9, 13
4, 5, 10, 10
4, 5, 10, 11
4, 5, 10, 12
4, 5, 10, 13
4, 5, 11, 11
4, 5, 11, 12
4, 5, 11, 13
4, 5, 12, 12
4, 5, 12, 13
4, 5, 13, 13
4, 6, 6, 6
4, 6, 6, 7
4, 6, 6, 8
4, 6, 6, 9
4, 6, 6, 10
4, 6, 6, 12
4, 6, 7, 7
4, 6, 7, 8
4, 6, 7, 9
4, 6, 7, 10
4, 6, 7, 12
4, 6, 8, 8
4, 6, 8, 9
4, 6, 8, 10
4, 6, 8, 12
4, 6, 8, 13
4, 6, 9, 9
4, 6, 9, 10
4, 6, 9, 12
4, 6, 9, 13
4, 6, 10, 10
4, 6, 10, 11
4, 6, 10, 12
4, 6, 11, 11
4, 6, 11, 12
4, 6, 12, 12
4, 6, 12, 13
4, 6, 13, 13
4, 7, 7, 7
4, 7, 7, 8
4, 7, 7, 11
4, 7, 8, 8
4, 7, 8, 9
4, 7, 8, 10
4, 7, 8, 11
4, 7, 8, 12
4, 7, 8, 13
4, 7, 9, 9
4, 7, 9, 10
4, 7, 9, 11
4, 7, 9, 12
4, 7, 9, 13
4, 7, 10, 10
4, 7, 10, 11
4, 7, 10, 12
4, 7, 11, 11
4, 7, 11, 12
4, 7, 11, 13
4, 7, 12, 12
4, 7, 12, 13
4, 7, 13, 13
4, 8, 8, 8
4, 8, 8, 9
4, 8, 8, 10
4, 8, 8, 11
4, 8, 8, 12
4, 8, 8, 13
4, 8, 9, 9
4, 8, 9, 10
4, 8, 9, 11
4, 8, 9, 12
4, 8, 9, 13
4, 8, 10, 10
4, 8, 10, 11
4, 8, 10, 12
4, 8, 11, 11
4, 8, 11, 12
4, 8, 11, 13
4, 8, 12, 12
4, 8, 12, 13
4, 8, 13, 13
4, 9, 9, 10
4, 9, 9, 12
4, 9, 10, 11
4, 9, 10, 12
4, 9, 10, 13
4, 9, 11, 11
4, 9, 11, 12
4, 9, 12, 12
4, 10, 10, 11
4, 10, 10, 12
4, 10, 11, 12
4, 10, 11, 13
4, 10, 12, 12
4, 10, 12, 13
4, 11, 12, 13
4, 12, 12, 12
5, 5, 5, 5
5, 5, 5, 6
5, 5, 5, 9
5, 5, 5, 12
5, 5, 6, 6
5, 5, 6, 7
5, 5, 6, 8
5, 5, 6, 11
5, 5, 7, 7
5, 5, 7, 8
5, 5, 7, 10
5, 5, 7, 11
5, 5, 8, 8
5, 5, 8, 9
5, 5, 8, 10
5, 5, 8, 11
5, 5, 8, 12
5, 5, 8, 13
5, 5, 9, 9
5, 5, 9, 10
5, 5, 9, 11
5, 5, 10, 10
5, 5, 10, 11
5, 5, 10, 13
5, 5, 11, 11
5, 5, 11, 12
5, 5, 11, 13
5, 5, 12, 12
5, 5, 12, 13
5, 5, 13, 13
5, 6, 6, 6
5, 6, 6, 7
5, 6, 6, 8
5, 6, 6, 9
5, 6, 6, 10
5, 6, 6, 12
5, 6, 7, 7
5, 6, 7, 8
5, 6, 7, 9
5, 6, 7, 12
5, 6, 7, 13
5, 6, 8, 8
5, 6, 8, 9
5, 6, 8, 10
5, 6, 8, 12
5, 6, 8, 13
5, 6, 9, 9
5, 6, 9, 10
5, 6, 9, 11
5, 6, 9, 12
5, 6, 9, 13
5, 6, 10, 10
5, 6, 10, 11
5, 6, 10, 12
5, 6, 10, 13
5, 6, 11, 11
5, 6, 11, 12
5, 6, 11, 13
5, 6, 12, 12
5, 6, 12, 13
5, 6, 13, 13
5, 7, 7, 9
5, 7, 7, 10
5, 7, 7, 11
5, 7, 8, 8
5, 7, 8, 9
5, 7, 8, 10
5, 7, 9, 10
5, 7, 9, 11
5, 7, 9, 12
5, 7, 9, 13
5, 7, 10, 10
5, 7, 10, 11
5, 7, 10, 12
5, 7, 10, 13
5, 7, 11, 11
5, 7, 11, 13
5, 7, 12, 12
5, 7, 13, 13
5, 8, 8, 8
5, 8, 8, 9
5, 8, 8, 10
5, 8, 8, 13
5, 8, 9, 11
5, 8, 9, 12
5, 8, 9, 13
5, 8, 10, 11
5, 8, 10, 12
5, 8, 11, 12
5, 8, 11, 13
5, 8, 12, 12
5, 9, 9, 11
5, 9, 9, 12
5, 9, 10, 10
5, 9, 10, 11
5, 9, 10, 13
5, 9, 11, 13
5, 9, 12, 12
5, 9, 12, 13
5, 10, 10, 11
5, 10, 10, 12
5, 10, 10, 13
5, 10, 11, 11
5, 10, 12, 13
5, 10, 13, 13
5, 11, 12, 12
6, 6, 6, 6
6, 6, 6, 8
6, 6, 6, 9
6, 6, 6, 10
6, 6, 6, 11
6, 6, 6, 12
6, 6, 7, 9
6, 6, 7, 10
6, 6, 7, 11
6, 6, 7, 12
6, 6, 8, 8
6, 6, 8, 9
6, 6, 8, 10
6, 6, 8, 11
6, 6, 8, 12
6, 6, 8, 13
6, 6, 9, 10
6, 6, 9, 11
6, 6, 9, 12
6, 6, 9, 13
6, 6, 10, 12
6, 6, 10, 13
6, 6, 11, 12
6, 6, 11, 13
6, 6, 12, 12
6, 6, 12, 13
6, 7, 7, 10
6, 7, 7, 11
6, 7, 8, 9
6, 7, 8, 10
6, 7, 8, 11
6, 7, 8, 12
6, 7, 9, 9
6, 7, 9, 12
6, 7, 10, 10
6, 7, 10, 12
6, 7, 10, 13
6, 7, 11, 11
6, 7, 11, 12
6, 7, 11, 13
6, 7, 12, 12
6, 7, 12, 13
6, 8, 8, 8
6, 8, 8, 9
6, 8, 8, 10
6, 8, 8, 11
6, 8, 8, 12
6, 8, 9, 9
6, 8, 9, 10
6, 8, 9, 11
6, 8, 9, 12
6, 8, 9, 13
6, 8, 10, 11
6, 8, 10, 12
6, 8, 10, 13
6, 8, 11, 11
6, 8, 11, 12
6, 8, 11, 13
6, 8, 12, 12
6, 8, 13, 13
6, 9, 9, 10
6, 9, 9, 11
6, 9, 9, 12
6, 9, 10, 11
6, 9, 10, 12
6, 9, 11, 12
6, 9, 11, 13
6, 9, 12, 12
6, 9, 12, 13
6, 10, 10, 10
6, 10, 10, 13
6, 10, 11, 12
6, 10, 12, 12
6, 10, 12, 13
6, 11, 11, 12
6, 11, 12, 12
6, 11, 12, 13
6, 12, 12, 12
6, 12, 12, 13
6, 12, 13, 13
7, 7, 7, 12
7, 7, 8, 11
7, 7, 9, 10
7, 7, 10, 13
7, 7, 11, 12
7, 7, 11, 13
7, 7, 12, 12
7, 7, 12, 13
7, 8, 8, 9
7, 8, 8, 10
7, 8, 8, 11
7, 8, 8, 12
7, 8, 8, 13
7, 8, 9, 10
7, 8, 9, 12
7, 8, 9, 13
7, 8, 10, 10
7, 8, 10, 11
7, 8, 10, 13
7, 8, 11, 12
7, 8, 11, 13
7, 8, 12, 12
7, 8, 12, 13
7, 9, 9, 13
7, 9, 10, 11
7, 9, 10, 12
7, 9, 11, 11
7, 9, 11, 12
7, 9, 12, 12
7, 9, 13, 13
7, 10, 10, 11
7, 10, 10, 12
7, 10, 11, 13
7, 10, 12, 12
7, 10, 12, 13
7, 12, 12, 13
8, 8, 8, 10
8, 8, 8, 11
8, 8, 8, 12
8, 8, 8, 13
8, 8, 9, 11
8, 8, 9, 12
8, 8, 9, 13
8, 8, 10, 12
8, 8, 10, 13
8, 8, 11, 12
8, 8, 11, 13
8, 8, 12, 12
8, 8, 12, 13
8, 9, 9, 12
8, 9, 10, 12
8, 9, 10, 13
8, 9, 11, 11
8, 9, 11, 12
8, 9, 11, 13
8, 9, 12, 12
8, 9, 12, 13
8, 10, 10, 12
8, 10, 11, 11
8, 10, 12, 12
8, 10, 12, 13
8, 10, 13, 13
8, 11, 12, 12
9, 9, 9, 12
9, 9, 10, 13
9, 9, 11, 12
9, 9, 11, 13
9, 9, 12, 12
9, 9, 12, 13
9, 10, 10, 13
9, 10, 11, 12
9, 10, 11, 13
9, 10, 12, 12
9, 10, 12, 13
9, 11, 11, 11
9, 11, 12, 12
9, 11, 12, 13
9, 11, 13, 13
9, 12, 12, 12
10, 10, 10, 12
10, 10, 10, 13
10, 10, 11, 12
10, 10, 11, 13
10, 10, 12, 12
10, 10, 12, 13
10, 11, 11, 12
10, 11, 11, 13
10, 11, 12, 12
10, 11, 12, 13
10, 12, 12, 12
10, 12, 12, 13
10, 12, 13, 13
10, 13, 13, 13
11, 11, 11, 12
11, 11, 11, 13
11, 11, 12, 12
11, 11, 12, 13
11, 12, 12, 12
11, 12, 12, 13
11, 12, 13, 13
11, 13, 13, 13
12, 12, 12, 12
12, 12, 12, 13
12, 12, 13, 13
12, 13, 13, 13  12+13-(13/13)=24