An interior designer has a dilemma. She has to move an amazingly heavy armchair which is up against a wall. The chair needs to be sitting so it is exactly beside its starting position and facing the same way.

If the only possible movement is to rotate the chair on any of its corners, how can the chair be moved to its new position?

(In reply to Imperfect Armchair Solution by nikki)

Why didn’t anyone correct me? My alternate problem and solution were very wrong =)

Consider a leg (pivot point) that is D away from the side of the chair. The perpendicular distance from the leg to the wall is shorter than the diagonal distance from the leg to the corner against the wall. Draw a circle with its center at the leg, passing though the corner of the chair against the wall. This is the path of the corner of the chair. Notice, I can’t rotate my chair on that leg, because I will be trying to push the corner of the chair into the wall.

Posted by nikki on 2004-09-13 15:55:05