House/Wilson Requests and Recs

Hello, I have a vague memory of a fic where either House or Wilson uses a take-home pregnancy test. He tests his own urine because there's a type of cancer that causes men to produce the same hormone that the pregnancy test detects. I don't remember anything else, which one did it, why, or whether it was positive or negative. Does this sound familiar or did I imagine it?

There were three fics, written years ago; I don't remember if the same author wrote all three of them, where they were posted, their titles, or who the author(s) was/were.  The central concept is that Earth is so overpopulated that half of the world's population must be culled.  The leaders have built a Machine to do this.  People go into the Machine in pairs: you can challenge someone to go into the Machine with you, or your opponent can be randomly selected.  The Machine somehow calculates which of the two is most worthy to live, and kills the other.  These three stories tell what happens when House, Wilson and Cuddy's turns come to face the Machine.  (If you haven't read these stories don't take the death/suicide tag as a spoiler, I put it there because by definition these stories are about death.)