Only display posts that are in category A, AND C AND D

I’m thinking about using WP as a kind of on-line schoolbook. In order to make it user friendly, it needs to be able to only show posts that are in more than 1 category.

E.g.
I have three categories. The categories are
– days of the week
– colors
– levels

Can a user select only the posts that are in the category’s white thursday?
And than see all posts that are AND in category white AND in category thursday.
Then narrowing it down to white thursdays of level 2?

Better even: then print the posts.

I don’t need a complete explaining how it would work, only if there’s some way to make this work (an existing plug in e.g.) Anyone know a site that has this feature?

Thank you