What are some mathematical problems that are feasible for preschool children to stimulate their intellectual development?

There are multiple natural laws that are not apparent to them, for example:

* the conservation of number/quantity,
* sets are not disjoint classes (i.e. might overlap),
* fallacy of circular arguments.

I posted the examples as answers, so they aren't privileged. Also, 
it would be great if we could have **one problem per answer**, so the votes would represent our opinions more precisely.

Finally, the ideas for the examples I posted come from a great book ["Math from Three to Seven"](http://www.ams.org/bookstore-getitem/item=mcl-5) by [A. Zvonkin](http://www.labri.fr/perso/zvonkin/), which I strongly recommend to anyone interested in this topic.

**Edit:** First, I would not ask a child a bare question. Some posts suggests games and games are great. In fact, all of examples I posted are easily transformable into games (the symmetry-related actually is a game already). In this light, the question could be understood:

> 
> If I had to ask a question or set a mathematical problem (in whatever form, game or not, that would be appropriate for the child), which questions and problems would be most suitable for a preschooler?
> 
> 
> 

I'm looking for *concrete examples*. Posts like "use another approach", or "use questions that arise because of natural situations", or "just let it play some Lego" are *not* valid answers. In other words, I *do* acknowledge Lego as a great educational toy/tool, but "Lego" by itself does not answer the question. If you insist on games, how and *which* mathematical ideas would you incorporate into your play?