Earlier quoted context omitted.
"Knowing how to code a mergesort" is specifically not what they're looking for, in my experience. The idea is to come up with a problem that requires an interesting algorithm that very few people will know, and see how the candidate reasons their way to an answer.
Are you saying they should be able to derive a little known algorithm by themselves? What do you make of Knuth's quote about how many people implement binary search wrong? http://en.wikipedia.org/wiki/Binary_Search#Implementation_is...
Who doesn't know that (x + y) / 2 can overflow?
But the people who you really want to filter out have no idea or intuition that a problem can be solved by slicing it into two. That's the key idea behind binary search (and indeed, much of computer science).