Wednesday Problem

I shall start a tradition of a Wednesday Problem. Thus every Wednesday I shall (try to) post a mathematical puzzle or an exercise. I will try to indicate the level of the problem on the scale 1-5, 1=simple, 5=advanced. High level does not imply that one needs prerequisites to solve the problem and low level does not imply the converse. But still the level will pesumably reflect my oppinion. In a nut shell: don’t take the level too seriously.

I will not generally publish any solution, but I can send/discuss the solution by e-mail with anyone who contacts me. My e-mail is vadim dot kulikov at helsinki dot fi.

Readers are encouraged to comment their remarks, solutions and questions concerning the problems.

If you have an interesting puzzle/riddle/problem, you can send it to me by e-mail and we might have the fun of sharing it in this blog.

The problem for today is an ancient problem, because I heard it already many years ago from Tuomas Orponen. It is:

Find an uncountable collection [tex]A[/tex] of subsets of natural numbers ([tex]A\subset\mathcal{P}(\mathbb{N})[/tex]) such that for every [tex]x,y\in A[/tex] either [tex]x\subset y[/tex] or [tex]y\subset x[/tex].

Level 2/5