# The three utilities puzzle

Here is a variant of the three utilities puzzle. Famously, It is impossible to solve it on a plane paper (Euler's theorem can prove that). But can you solve it on a coffee mug?

Connect all three utilities to each of the houses, such that no two lines intersect.


Don't draw on the inside, It's for drinking ofcourse.

• There seems to be a conflict between not citing the source of this puzzle, and the spam policy. However, since I think there are very few of us here who wouldn't want to enjoy their coffee made with well connected heat, electricity and water, here's the link: mathsgear.co.uk/products/utilities-puzzle-mug – Bass Dec 25 '17 at 12:38
• @Bass, I saw these mugs with one of my colleagues. So I didn't knew if they were mass produced. I will add it to the question. No worries. – prog_SAHIL Dec 25 '17 at 12:59

When trying to connect all utilities $A$, $B$ and $C$ to the three houses one realizes that

one needs just 1 "crossing" of lines (see drawing). This can be done on a topology like a mug (or donut) by having one of the lines going on the handle of the cup and the other one through it.

And this is how it looks like on a cup:

Yes, you can, just...

use the handle to jump over a line you would have to cross on a plane.