How many checkmate situations?

Here has been discussed asbout how many different chess games there are and the number was something like 10^120 if I remember. Could someone estimate how many different chekmate situations there are?

A bzillion

Most would be nonsense positions, so it's just a tedious math question.

If you removed all the pieces not involved in the mate  you could do something like there are 11 different types of pieces that can control the 8 squares around the enemy king (when it's not on the edge). Roughly half of these will be one of 6 enemy pieces which will sometimes have a choice of many squares. I'll estimate about 6 different choices on average. Then multiply by all non-edge squares (49) and the mating piece (one of 5 types) and things like this and I get about 10^13

Some of those positions would be illegal though, and some would be rotations, but obviously this leaves out a lot of positions too, like where one piece controls more than 1 square around the enemy king, or when a king is on the edge of the board.

Also 10^120 is a rough estimate for unique games, not unique positions. For example a game may repeat a position, or two games may be mostly identical except for slightly different move order.

Unique positions is estimated more like 10^40

exactly two. you are either in checkmate or you are not. ;-)

This was good one... :)