Once we finally got the many layers of carpet up, we discovered
that the concrete floor is covered throughout with vinyl tiles.
Now, basically, these provide a decent surface for laying new
surfaces (carpet/laminate/whatever) on, and I really don't want to
lift the lot of them. However, some of them have broken and come
away (mostly where the previous carpets were nailed down), so I'm
left with a 1/2-tile. I'm hoping to fill the gaps with a
self-leveling compound of some sort. Does anyone have any
recommendations of what to use, or is this a stupid thing to be
attempting?

Many thanks!
--
Selah