24点算法技巧不少于四种方式

24点游戏是一种经典的数学智力游戏，目标是通过加减乘除四种运算，使得四个数字的结果等于24。以下是不少于四种不同的解题技巧：

技巧一：优先考虑乘法和除法

由于乘法和除法的优先级高于加法和减法，通常优先考虑这两种运算，因为它们能更快地得到较大的结果。

例子： 3, 8, 2, 4

8 3 = 24

然后可以用24除以剩下的两个数来得到24。

技巧二：利用括号改变运算顺序

有时候，通过添加括号可以改变运算的顺序，从而找到解决方案。

例子： 2, 6, 3, 8

2 (8 3) = 2 5 = 10

10 6 = 60

60 24 = 36（错误）

修改为：2 (8 3) 6 / 2 = 24

技巧三：寻找“倍数”关系

如果发现四个数字中有两个数字的乘积或商是另一个数字的倍数，可以利用这一点。

例子： 1, 2, 4, 8

1 8 = 8

8 2 = 16

16 4 = 64

64 / 8 = 8

8 2 = 16

16 1 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 = 16

16 2 = 32

32 / 4 = 8

8 4 = 32

32 / 2 =