Single post from each category, with date

Hi,

I have thirteen categories on my blog, and I’d like to do a page which lists each category name, and under this has the most recent post title with a link and either the date or (preferably) “xx days ago”.

How would I do this in a loop? I’ve tried for a few days but can’t figure it out.

Just need to list all my categories, and the most recent feed from each.

Thanks in advance,
deblaca