Can the mouse eat the cube?
A mouse eats its way through a 3*3*3 cube of cheese by tunnelling through all of the 27 1*1*1 subcubes. If he starts at one corner and always moves on to an adjacent uneaten subcube, can he finish at the center of the cube?

More on Primes

Prove that there is atleast one prime number between n and 2n.

Consecutive no-prime numbers
Tell me 1000 consecutive non-prime numbers.

I am not naming this! Well, I name it
Handshakes
At a recent convention of Scientists, there was a lot of handshakes between the scientists. But the number of Mathematicians in attendence who shook hands an odd number of times was even, why?! Remember that an handshake requires exactly two different people!

The Frog and the Wall
Suppose there is a frog at a certain distance from a wall, say, ten feet. Imagine that this frog jumps halfway to the wall, so that he is five feet away. Suppose he continues to jump toward the wall, each time getting halfway there. Will the frog reach the wall?

Another Question will follow in this context!