1) 4 matches are arranged as shown. They represent a cocktail glass, the match head in the middle is an onion. Problem: Move only two matches so the glass is reformed but the onion, which must stay where it is, is outside the glass. The glass may change it direction or position. The upper right figure is not a solution because the onion is still inside the glass. The lower right version isn't either because three matches were moved.

2) Problem: Move the queen four times, making standard queen moves (horizontally, vertically or diagonally), so that she passes through all nine of the shaded squares. The shown solution is not valid because it uses six moves!