The door puzzle.

Hint 1 of 4:

The puzzle is to slide the colored pegs so that they line up with their
corresponding colored arrows.

Hint 2 of 4:

Moving a peg slides it into the empty slot, if one is next to it.

Hint 3 of 4:

Imagine that the slots are numbered as follows.  The three to the upper left
are 1, 2, and 3, 1 being the outermost one.  The three to the upper right are
4, 5, and 6, 4 being the outermost one.  The lower three are 7, 8, and 9, 7
being the outermost one.  10 is the one to the lower right.