1) is trivia/trick question (obviously designed to catch those who learned the squeeze theorem as the sandwich theorem), 2) is hilariously simple, 3) is trivial, 4) is trivia, 5) is interesting.
Anyone have access to the harder, non-trivia(l) questions please?
[edit] found a few more from 2013, which I think are more interesting: http://digitaleditions.walsworthprintgroup.com/display_artic...
For (2), imagine if there were only two teachers in the convention and they shook hands with each other once - that invalidates option C. If they shake again, that invalidates option B and E. A and D both talk about an even number of teachers, so let's imagine there were three teachers. If each teacher shakes hands with the other two once, that invalidates D. So A is the answer. I guess some form of graph theory is involved with solving it properly.
(3) can be reasoned in the same way by imagining quadrilaterals for each option. A quad with two adjacent tiny edges and two long edges symmetric along one axis (like a square with one vertice pulled away) gives a rectangle, which invalidates A, B and E. Making it asymmetric by moving the far vertex invalidates C. So only D is left.
Who says there's that exactly one of the answers is right? For (2) the formulation of the question even suggests that any number could be right or wrong.
Edit: And yes, I know the inability to find counter-examples to something doesn't necessarily mean it's true.
Now clearly if the main teacher having odd shakes x, implies that an odd number of other teachers have odd total shakes, then the total odd shakers is even.
I'd generally be inclined to agree, and I think that there are too many people on HN that constantly call legitimately hard things trivial, which I dislike. But in this case, the two that I referred to as such are actually solvable by an eleven year old. I refuse to believe that any quants -- a profession known to be composed of some of the smartest people on earth -- have any difficulty whatsoever with these problems.
If they were in a book of brain teasers, I wouldn't go through the book and laugh at how "trivial" all the questions were, that would make me a dick. But these are questions asked to goddamn quants, and in that context these questions are certainly hilariously simple.
So it would have taken rather more tries to find 18...
I believe the event was a fundraiser for a kids-friendly math museum, so I'll cut these guys a lot slack. No matter how they did, they had to whip out their checkbooks at the end of the evening.
Shouldn't the "Fermat" part rule out the squeeze theorem? I know Fermat did work that contributed to the development of Calculus, but he was gone long before either Newton or Leibniz published.