算24点，到底有多少种组合是可解的

对于算24点，想必大家都是知道的。简单说来就是拿一幅扑克牌，随机抽取四张，然后根据这四张扑克牌上的数字利用“加减乘除”算出24来。只能运算四次而且四张扑克牌都必须用到。小编以前觉得自己的24点算的还是挺不错的，结果直接被秒杀。

言归正传，既然是随机抽取4张扑克牌，那自然就面临一个问题：所有的任意四张扑克组合都能算出24点吗？

当时自己头脑不清说都是有解的，还说有个paper证明了这个。今天在办公室找到了自己昨天晚上说的paper。好吧内容不太一样，那个paper说的是关于abc猜想的，其中引用了一点关于算24点的东西，但是结论和算24点没有一点关系。是我胡说八道了，道歉道歉。（所以在引用reference的时候要查证啊！）

今天晚上，其实就是刚才，从学校回来闲着没事就试图证明一下到底是不是任意四张扑克都能算出24点。结果显然是不对的，比如很简单的反例，1 1 1 1 就不可能算出24来。

那问题自然就变成：到底多少种组合有解？

这个题设用一般的数论方法反而没有什么可下手的地方。但是，一共才52张扑克牌。。。任意抽取4张，不考虑花色的话就只有1820种组合而已。所以，当然不能用手慢慢的算，我就写了个简单的matlab程序求解到底多少组合有解。

matlab的程序很简单。其实就是枚举法。。。从头试到尾。。。

计算显示算24点的话，1820个可能的抽取方法里面有1362种都是可解的。

所以说，如果你足够牛的话，把1362种可解方法背下来，你玩24点就无敌了。

其实我们不止可以算24，算23啊22啊都是可以的。下面我列出了对于点数1到31的可解组合数：（大家可以按照几天几号就算多少点来玩。。。杜绝作弊的可能哈哈）

There are 1580 combinations have solution for 1 point calculation.

There are 1758 combinations have solution for 2 points calculation.

There are 1651 combinations have solution for 3 points calculation.

There are 1612 combinations have solution for 4 points calculation.

There are 1581 combinations have solution for 5 points calculation.

There are 1590 combinations have solution for 6 points calculation.

There are 1542 combinations have solution for 7 points calculation.

There are 1534 combinations have solution for 8 points calculation.

There are 1540 combinations have solution for 9 points calculation.

There are 1540 combinations have solution for 10 points calculation.

There are 1486 combinations have solution for 11 points calculation.

There are 1535 combinations have solution for 12 points calculation.

There are 1414 combinations have solution for 13 points calculation.

There are 1449 combinations have solution for 14 points calculation.

There are 1440 combinations have solution for 15 points calculation.

There are 1424 combinations have solution for 16 points calculation.

There are 1240 combinations have solution for 17 points calculation.

There are 1397 combinations have solution for 18 points calculation.

There are 1197 combinations have solution for 19 points calculation.

There are 1372 combinations have solution for 20 points calculation.

There are 1254 combinations have solution for 21 points calculation.

There are 1244 combinations have solution for 22 points calculation.

There are 1108 combinations have solution for 23 points calculation.

There are 1362 combinations have solution for 24 points calculation.

There are 1074 combinations have solution for 25 points calculation.

There are 1163 combinations have solution for 26 points calculation.

There are 1136 combinations have solution for 27 points calculation.

There are 1171 combinations have solution for 28 points calculation.

There are 942 combinations have solution for 29 points calculation.

There are 1193 combinations have solution for 30 points calculation.

There are 890 combinations have solution for 31 points calculation.

把这些可解数画出图来，算24点，到底有多少种组合是可解的？

发现随着点数的增加，可解的组合数也随着减少。再算2点的时候的可解数最多。所以果然，2就是最2的啊！！

所以，大家都来算2点吧～～～～

来源：数学中国

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