Latest post from multiple categories?

Hi
I want to do a front page as a magazine masonry layout with 24 posts, one each from 24 categories:
– Each post is the latest post in one category.
– (there is only one post shown from each category)
– The latest post goes to the top of the page.
– (also, each category should be seen on each post as a link)

There are 24 contributors (via Postie, which creates a post to a specific category based on the email it came from).

This way there is competition between the 24 contributors, so the latest post from a particular contributor will go to the top of the page. Its an attempted cure for laziness.

Any thoughts if this is possible?
Marek