Most cafeteria water dispensers will let two (sometimes more) people fill a jug at the same time. This article uses simple maths to prove that it’s a waste of time. In other words, two people should never use the same water dispenser at the same time: I call this the *cafeteria paradox*.

## An intuitive presentation

Let’s start with a little brain teaser:

Alice and Bob are at the cafeteria, seating at different tables. Alice stands up to refill her table’s water jug. Little after, Bob stands up with his own table’s jug, heading to the same water dispenser. That water dispenser is a perfectly standard one, with two taps, and Bob finds himself standing near Alice. After a small hesitation, Bob starts using the second tap to fill his own jug, thereby diverting part of the output previously devoted to Alice.

This grants him an exasperated and somewhat puzzled look from Alice. Why?