### Russell's Paradox

Following on from yesterday's post, I thought I might explain a bit about the problem Russell discovered with set theory.

**( Russell's Paradox, with tentacles. )**Following on from yesterday's post, I thought I might explain a bit about the problem Russell discovered with set theory.

**( Russell's Paradox, with tentacles. )**

Unless you've been living under a rock, you've probably encountered the "men have more sexual partners than women" paradox at some stage. If you haven't, the gist of it is this: surveys that ask men and women about how many opposite-sex partners they've had in their lifetime generally find that the typical man has almost twice as many as the typical woman. (See this NY Times article for some examples.)

What is going on here? If our population is roughly 50/50 male/female, a naive look at the situation tells us that the numbers should be equal; any time a new couple forms up, both those figures should go up by the same amount, right?

There are several factors that contribute here. Some of them are well-known and get trotted out every time this sort of thing comes up, but there's a sneaky one that hardly ever gets a mention and really should.

**( The standard ones: sampling error, reporting error, mean vs median. )**

**( The sneaky one. )**

What is going on here? If our population is roughly 50/50 male/female, a naive look at the situation tells us that the numbers should be equal; any time a new couple forms up, both those figures should go up by the same amount, right?

There are several factors that contribute here. Some of them are well-known and get trotted out every time this sort of thing comes up, but there's a sneaky one that hardly ever gets a mention and really should.

Via **hasimir** and various others: a self-referential multiple-choice test! Your challenge is to fill it out so that all 20 answers are correct at the same time.

BTW, with every answer you click it updates to show which are right and which are wrong. This refers to the*current* status of the other questions, not the final correct answers. For instance, question 3 asks how many questions have answer E; if you answer C (i.e. two 'E's), this will show up as correct when you have exactly two 'E's ticked on the test and incorrect otherwise.

And yes, it is solvable with a little bit of pen-and-paper work.

BTW, with every answer you click it updates to show which are right and which are wrong. This refers to the

And yes, it is solvable with a little bit of pen-and-paper work.