MATHEMATICS

For the beginning try to solve this easy one:
If X and Y are digits of the number: 5109094X1717094400Y0 , 
and it is true that 5109094X1717094400Y0 = 21·20·19·18·....·4·3·2·1 
then what are the digits X and Y?

Another one VERY VERY hard!

Consider the 3 following persons: A1,B1,B2

A1 told to B1 and B2:
"I have thought 2 integer numbers (1,2,3,4,....). Each of them is bigger than 1 while their sum is lower than 100. And now i will tell ONLY to B1 the product of the 2 numbers. And then i will tell ONLY to B2 the sum of them."
So what A1 said, happened......

Now the following conversation between B1 and B2 occured:

B1:"As it seems i can't say what the numbers are."
B2:"I knew from before that you couldn't!"
B1:"Oh really? If this is the case, then i know what the numbers are!"
B2:"Hmm, so i know them too!"


If A1,B1,B2 say only the truth, then what are the numbers?
-------------------------------------------------- Another tricky: You have a set of people in a house. These people have n hands? How many are they?

1)Half of n
2)Half of (n+1)
3)Half of (n+1) if n is odd and Half of n if n is even
4)Nothing of the above

--------------------------------------------------

Mathematica 5.0!
Matlab 7.0.1! NEW
Maple 9!
SciLab! (Free!)
Maxima 5.9.1
Virtual Calc 2000. Supports an
Origin 7.5! Top Graphing Program.
DCProof. (Free!)
My program that plays a perfect NIM game.

Math related links..........

Everything about Mathematics!
Great site with millions of Math puzzles!
SCI.MATH Forum...............
Hilbert's Problems......
Unsolved problems Goldbach Conjecture!
Unsolved problems Riemann Hypothesis!
Unsolved problems Collatz Conjecture!
Unsolved problems Collatz Conjecture
Unsolved problems 196 Algorithm.
Unsolved problems 196 Algorithm.
Mensanator's Homepage.
Nice mathematics page....!
Nice mathematics page....!
Isopikon (An amazing drawing tool for Euclidean Geometry) and other......
Proof that Pi is irrational.
Nice overview of Godel's incompleteness theorem.
Godel's Incompleteness Theorem!
Pi234c!
QuickPi!
Mathematical Logic page.