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There is a particularly annoying puzzle that goes something like this:

"A rooster sits on the apex of a barn roof. The roof pitches at an angle of 43 degrees above the horizontal and is made of wood painted red. On the northern side of the roof, there is a large tree which casts a shadow over most of the roof. On the southern side, there is a duck pond. There is a very light rain shower falling, and the wind speed is 20 km/h from the Southwest. It is 10:47am on the 19th of August and the current temperature is 14 degrees celsius. The rooster lays an egg. Which way does it roll?"

The correct answer to this puzzle is usually given as: "Roosters don't lay eggs."

I take offense at this for several reasons:

Firstly, whenever I have seen anyone ask this puzzle, they have seemed to delight in watching the other person squirm, and they have had a superior "You're so stupid that you haven't figured it out" expression on their face. In my book, you are the worst sort of asshole if you choose to do things simply to make yourself feel superior to someone else.

Secondly, the puzzle didn't ask to evaluate whether it was possible for a rooster to lay an egg in this situation! No, it asked to find which way the egg rolls if indeed the rooster did lay an egg. Sure you could discuss whether it was possible, but that doesn't change what you've been asked to do.

My goodness, I know so many puzzles where the situation described is impossible or extremely unlikely, and it never stops people from figuring out the answer anyway. Just how likely IS it that a man has to take a cabbage, a goat and a wolf across a river in a small boat? Yet people have been posing and solving this problem for hundreds of years!

On a more serious note, almost none of the problems we give students are 100% realistic. In Physics courses, the students get problems about objects being dropped down holes drilled to the centre of the Earth. In Economics courses, they do problems that concern people who only consume nuts and bananas. In Architecture, they get volume and area problems with only whole-number answers. None of these situations is actually possible in real life, but that doesn't stop us from expecting the students to do them anyway, because we know it will help them learn if they do. Are we really going to allow people to declare the imposibility of the situation and on that basis refuse to do the problem?

And finally, as a pure mathematician, I am always solving problems in situations that are so-called impossible – imaginary numbers,  four dimensional space, projective space where there are no parallel lines, finite fields where 1+1 = -1 ...

So in the end, I don't think it matters that roosters don't lay eggs!