I had read a problem at Polish Olympia in Information.
The problem is give you N strings that composed by 0 and 1.
And ask you is there exist a infinite string composed by 0
and 1 exclude those N strings.
For example:(first line is the number N.)
3
00
01
11

the answer is NO.
because the infinite string doesn't exist.
it seems so hard that i could'n find the trick...
is there anybody have a good idea?

First of all you don't mention what is the max N also what
is the max string length.Please post the url to the
complete text of the problem.

Now for the problem.The first thing that comes to tought is
to try to find such string of length = the max string lenth
of the input that extended by the same string doesn't
contain any of the input strings.If we can find such string
then we can be sure that there is infinite string not
containing the input string.This is my first idea I didn't
prove that not being able to find such string means that
there doesn't exist an infinite string satisfying our
requirements.

The url is
http://www.mimuw.edu.pl/OI/english/oi7/wirusy.html
I think there might be a formula about this problem, but
I'm not sure.