Math Questions

[charlie]

Ok.. I need some serious help from some of the Math gurus on here. In my Math for Liberal Arts Majors class, the TA has said that anyone who can solve this problem will get an A in the course-- so, if anyone can help me out with it, it will be much appreciated. He says the answer is a very long one, about 4 pages worth. So, if someone can come up with the correct answer, I am willing to put forth some sort of compensation.

On to the question:

There is a magician who has 100 cards, numbered 1 through 100. He has 3 boxes labelled A B & C. He asks a participant to select two cards, from separate boxes, and tell him the sum of the two numbered cards. From this, he can determine which box was NOT picked. The question is, how many different ways can he put the cards in boxes, such that this trick will work every time.

[ross]

You can find the answer here:

http://www.maa.org/features/mathchat/ma ... 17_00.html

That page only gives the answer though, no in-depth proofs. I imagine it would be relatively easy to prove that the answers they give are correct. What would be most difficult is proving that all other combinations are not valid. You could search the web and see if anyone has a full proof out there. All I did to find it was paste the following into Google:

There is a magician who has 100 cards