Math puzzles suitable for printing on a mug

Question

I need to design a cup for a reception for first-year college students and i'm searching for some challenging and entertaining math puzzle or game to use. Previous years it has been used the "Three Utilities Problem", but i'm looking for something different or (at least) less known.

So far I have thought about:

• Nine Dot puzzle

• Some Tessellation puzzle

Do you know another Puzzle or game of this style ? (that can be printed on a cup)

Thanks in advance

Answer 1

Finally, i've used a Hex gameboard for the mugs

This is the final result:

Thanks for all your answers!

Answer 2

Challenge: divide the surface of the mug into seven connected regions such that each one is adjacent to the other six. In other words, embed $K_7$ on a torus.

Answer 3

A "How many squares" puzzle can easily be printed on a cup.