Fun Problems!!! (Always under construction)

Here are some problems that have I have been asked over the years that I find very interesting and, in some cases, quite entertaining to figure out. At the very least, you can become the light of any party with the power to shock and awe your friends with (sometimes) easy solutions to seemingly impossible problems. OK, so maybe I'm exagerating a little. In any case, I hope you enjoy.
Each link below consists of the statement of the problem, some hints, (lets face it, we all need help at times), and then, finally, the solution. If you have any problems of your own you find interesting and would like to add to the list, please send me the information. ENJOY!!!

The Problems:

Old Time Game Shows (Easy)
Determine the polynomial. (Easy)
Which number is the larger? (Moderate - requires knowledge of calculus, unless you can come up with a solution I've never seen!).
Who took my seat?! (Moderate)

If you are interested, here are some interesting false proofs based on calculus..... can you find the problems with the arguments?!

Obviously False Proofs... and by obvious, I mean they can't possibly be right since their conclusions are ridiculus!