A puzzle, from arpatubes.net.
There's no trick here. Still, only twenty percent of the people answering it have gotten it right, because it's the sort of thing you have to read very carefully.
The comments at fark.com (where I found this puzzle) are interesting. One common theme seems to be "this isn't really a math problem, this is a reading comprehension problem" or "this is a logic problem". But reading comprehension and logic are, of course, large parts of mathematics. I have a sense I'm preaching to the choir here.
On a similar but less frivolous note: from Pencils Down, A Letter to a Young Mathematician is a (fictional?) answer to what seems to be a student asking "what good are proofs?" (From vlorbik.) I'm reminded of the recent book Letters to a Young Mathematician, by Ian Stewart (who also wrote Does God Play Dice?; the resemblance of titles is almost certainly intentional. I suspect that students would, for the most part, feel differently about proofs and other things that aren't just rote calculation if they were introduced from the very beginning of their mathematical training, before they get the idea that all mathematics is arithmetic. But this might not be possible, because abstract reasoning is something that young children just aren't capable of, yet we need to start getting arithmetic into them at a young age. Their brains haven't matured enough yet for abstract reasoning.
As it is, students seem to resent being asked to prove something. A large part of this seems to be that proofs often require writing words, and mathematics, they feel, does not properly involve words. I actually spend a fair bit of time trying to counteract this in my teaching, but I can only do so much insisting that calculus students should know how to write complete sentences and be able to clearly explain their logic before they start to rebel.
And there is of course the problem that many students probably learn their first mathematics from an elementary school teacher that never much liked math when ey was in school.