Right Face is a puzzle made by Palmer Mebane, and many of the rules are paraphrased or taken from his blog at mellowmelon.wordpress.com. A robot begins on the square marked with a red arrow, facing in the arrow’s direction. It will proceed forward until the square ahead of it is a wall or one it has visited before. When that happens, it will first try to turn right (hence the puzzle name) and proceed forward. If the square ahead of it is still a wall or one it has visited before, it will go back and try to turn left instead. If it cannot do that either, it stops. The object is to determine which of the grid squares are walls such that the robot visits every grid square not marked as a wall before stopping. Some objects in the grid are given. Black boxes represent walls given to you. Black dots represent squares that cannot have a wall. Arrows also cannot have walls, and additionally when the robot steps on the arrow it must travel in the arrow’s direction on its next move. Note that this is a condition on you, not the robot. The robot will proceed with the instructions in the first paragraph regardless of the square, and it’s up to you to make it move in the right direction on arrowed squares. In particular the robot’s first step from the red arrow must be forward. Finally, the robot’s path must end on a square with a dot. In a puzzle in which no red arrow is given, one of the black arrows should have actually been made red. It is up to you to figure out which one.
See the sample puzzle below for any clarifications, or ask in the comments if you are confused