I would like to share following two mathematical problems which were brought to my knowledge by different people.
Statement of the problem is:
X has two children. Find the probability that:

Both children are girls, given that the older child is a girl.

Both children are boys, given that at least one of them is a boy.
Some historical reference can be found at Wikipedia: http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Also you can refer to this interesting paper published on this problem by Peter Lynch : http://mathsci.ucd.ie/~plynch/Publications/BIMSTwoChildParadox.pdf
 The twelvecoin problem by Sagar Shrivastava
Statement of the problem is:
There is a pile of twelve coins, all of equal size. Eleven are of equal weight. One is of a different weight. What are minimum number of times one need to weigh to find the faulty coin and determine if it is heavier or lighter?
Some historical reference can be found at this wikipedia page: http://en.wikipedia.org/wiki/Balance_puzzle
Also, a discussion on this problem is available at: http://mathforum.org/library/drmath/view/55618.html