This is a blog for students of MAT 157.
We should be able to communicate mathematics in this site. For example, we can discuss

$\lim_{x \rightarrow 0} \sin \frac{1}{x}$.

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1. Yevgeny Liokumovich

Here’s a modification of an old and famous puzzle.
It may seem very difficult, but it becomes much easier if you phrase it in terms of certain simple operations with functions.

You’ve been thrown into a dungeon with 100 wizards. There are two doors leading from the dungeon: behind one of them there is an enormous spider with long poisonous fangs that will jump on you and then slowly eat you. The other door leads to freedom, but you don’t know which of the two.
You know that 49 of the wizards always tell the truth and the rest always lie, but you don’t know which is which. You are allowed to ask only one wizard only one question.

Will your question be different if 50 wizards lie and 50 tell the truth?

Hint: The wizard that’s always telling the truth is like a function that given 1 outputs 1 and given -1 outputs -1. The wizard that always lies is like a function that’s doing the opposite. What operations can you do with these functions?