points.

$1.$ Give a complete problem formulation for each of the

following problems. Choose a formulation that is precise

enough to be implemented.

$1.$ There are six glass boxes in a row, each with a lock.

Each of the first five boxes holds a key unlocking the next

box in line; the last box holds a banana. You have the key

to the first box, and you want the banana.

$2.$ There is an n$\backslash$times n grid of squares, each square initially

being either an unpainted floor or a bottomless pit. You

start standing on an unpainted floor square and can either

paint the square under you or move onto an adjacent

unpainted floor square. You want the whole floor painted.