Here's a few good puzzles [not all maths related]:

1) From statistical records, what is the most dangerous job in America

2) If an American Airlines plane is flying in German airspace carrying Japanese businessmen for passengers, and it crashed on the Belgium/Germany border, exactly in the middle, where would they bury the survivors?

3) If you want to win the lottery jackpot, is it better to put £1 on every week for a year, or £52 at once? [include your reasoning; I've had arguments for months over this one]

4) [one for the chemists/physicists] Why are windows in old churches thicker at the bottom?

5) You are given nine coins and a weighing balance. You are told one of the coins is counterfeit and heavier than the rest - so, with just two uses of the balance [i.e. two weighings] is it possible to idenify the counterfeit? How?/Why not?

I'll post more when I can think of them.

2) You don't bury survivors!
4) Glass is a viscose liquid, it is not solid, so it will flow, and over time become thicker at the bottom. Churches are quite old, so show this effect.

I'm too tired to think solutions to the rest at the moment

Well done Julian - soooooooo many people have said 'you bury them wherever it crashes' it gets funny.

4 is of course correct

5 is actually quite a nice problem

If you are in a race and you overtake 2nd place. What place are you in?

Two cases for andy's problem.

Case 1
You are in third place to start with - you overtake second place, this puts you into second place.

Case 2
You are in first place and you 'lap' second place - you remain in first place.

So you are either first or second, depending on how you see the problem

Is the right answer. Got any of your own?

Try this....

You have 9 coins, but are told one of them is counterfeit and heavier than the others.
You are also given a weighing balance.
Using the weighing balance JUST twice, can you identify the counterfeit?

If so, how?
If not, why not? - give reasoning

PS - this is a simple combinatorics question

An even easier solution. Go to the shop and spend them all. That way you get more and have less hastle.

...Or you call the coins A,B,C,D,E,F,G,H,I.

Weigh: ABC-DEF and 3 cases result (balance, ABC heavier, DEF heavier).

Case one: weigh G-H. If they balance then I is the counterfeit, else the heavier of G and H is the counterfeit.

Case two: Weigh A-B. If they balance then C is the counterfeit, else the heavier of A and B is the counterfeit.

Case three: Weight D-E. If they balance then F is the counterfeit, else the heavier of D and E is the counterfeit.

Correct, nice one - didn't take too long

Any of your own?