两个避孕套组合问题(Two-Condom Combinatorial Problem)

from my life as a quant & 宽客人生

Problem:

Two (heterosexual) couples decide to have group sex with each other in all possible male-female combinations. They have only two condoms, and everyone is scared of catching some venereal disease. How can they manage four couplings with only two condoms?

问题：

两对（异性恋）情侣决定相互之间用所有可能的男女组合进行一次群体性交。他们只有两个避孕套，而且每个人都很惧怕得上某种性病。他们怎样才能用两个避孕套进行四次性交呢？（即甲女和甲男，乙男各一次，共计2次；乙女和甲男，乙男各一次，共计2次，一共4次性交）

Solution:

• The first man puts on two condoms, one over the other, and then sleeps with the first woman. Only the outer surface of the outer condom and the inner surface of the inner one has had contact with any potentially infectious surface.

• The man removes the outer condom and sleeps with the second woman.
• The second mand then dons the removed outer condom whose inner surface has until now had no contact with anyone's skin, and sleeps with the first woman, whose only contact has thus far been with the outside of the same condom.
• Finally, the second man dons the second condom over the one he is already wearing, and sleeps with the second woman, who again only experiences a condom she has already touched.

答案：

1. 第一个男人应该先带上两个避孕套，一个罩在另一个上面，然后和第一个女人性交。这样，只有罩在外面的避孕套的外表层和罩在里面的避孕套的内表层，接触到可能带有传染病的部位。
2. 之后第一个男人褪掉罩在外面的避孕套，与第二个女人性交。
3. 第二个男人接着戴上刚才褪下的罩在外面的避孕套，这个避孕套的内表层到现在为止还没有跟任何人的皮肤接触过，第二个男人戴好后跟第一个女人性交。而第一个女人直到现在还是只跟同一个避孕套的外表层发生接触。
4. 最后，第二个男人把第二个避孕套戴在他已经戴上的原先罩在外面的那个避孕套的上面，与第二个女人性交。而第二个女人也是只接触到那个她已经触碰过的避孕套。

很难抵挡住试图把这一问题推广到N对情侣的诱惑。