The so-called "tackless strip" is a medieval torture device. Despite its name, it in fact consists of nothing but sharp tacks designed to place themselves in such a way that you puncture yourself whenever you pick up the bloody things, whenever you put your hand down, or whenever you slip and fall. And despite the claims that they can be nailed down into wood or concrete, they don't seem to work on concrete at all. On the recently poured concrete, the nails just cause the concrete to crumble, leaving large holes that don't hold anything in place. And on the old concrete, the nails don't go in at all; they just bend.
The carpet pad is now down, thanks to bsittler and linley. Next: the carpet itself!