The Lemon Fool

A kitchen has an uneven floor. There are no steps but the continuous random waviness of the floor is such that when one tries to place on it a small square table with four legs, one leg is usually off the floor, causing the table to wobble. If one doesn't mind the table top being at a slant, is it always possible to find a place where all four legs are firmly on the floor? Or can a floor wave in such a way that no such spot is available? The four table legs are equal in length.

Cinelli

Get a three legged table?

Spoiler

Yes.

Place the table so that it wobbles on two opposite legs (the only way it can wobble!).
Rotate the table so that it wobbles on the other two legs.
As you rotate the table, there will be a position where the wobble changes from one pair of opposite legs to the other pair. At this position, all four legs will be on the floor so the table will not wobble.


Julian F. G. W.

Well solved, Julian. That is a beautifully concise way of answering the question.

Cinelli