Answer to
old chestnut: remove 2 matches to leave 2 squares:
___ ___
| |
| |
| ___|
| | |
| | |
|___|___|
Aye, there's the rub! You have to leave one big square and one small one or you'll never solve this puzzle.
For the second puzzle:
___ ___ ___
| | | |
| | | |
|___|___|___|
| | |
| | |
|___| |
| | |
| | |
|___|___ ___|
Note that the two solutions are inconsistent with one another... the former solution counts the big square which has a smaller square contained within it, while this one ignores it and thus counts 6 squares instead of 7.