List them here! You don't need to post an answer to a problem but post a problem if you have one.

Here's one I like : you begin with four points in the plane; initially they are at the vertices of a square. Then you may any point "jump" over another : i.e., drawing the line going through two points A and B, you can take A and move it to the other side of B so that the resulting point is on the line, and at the same distance from B than A was originally. You are allowed to do this as many times as you want and in any combination possible.

The question is : can you get a bigger square? Say how or why not.

Here's my favorite chess puzzle : move 29, black to move.
The game is Celso Golmayo Zupide vs Sam Loyd (1867).
I find it amazing, incredible. (I'm an amateur chess player).

Edit: Oh... I've just realized it's not a forced mate... but still, quite amazing finish.
May have I more luck with this game : black to play, move 43 : http://www.chessgames.com/perl/chessgame?gid=1070222. This time I think all the following moves are forced, until the lost (not the checkmate). So try to find black's winner move at move 43.
And to put the cherry over the cake, (the most amazing game in my opinion) : the entire game. I don't know if white's 24 th move is the winner move but if it is, then this is one of the harder puzzle one can find. So put the position at move 23 (just when black played) and try to guess what follows. (if you guess correctly white first move, you'll be surprised of his second move! And so on!). Game : http://www.chessgames.com/perl/chessgame?gid=1011478.

__________________
Isaac