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# Utilities puzzle mug

## £16.00

OK, so you might have seen this puzzle before but the chances are you've only ever tried to solve it in two-dimensional Euclidean space (on a bit of paper). But topology is everything when it comes to the Utilities Problem. That's why we've printed it on a mug. The challenge is to join all the houses to all the utilities without any of the nine lines crossing.

If you've tackled this one before you'll know it's very hard to solve (in fact, it's as hard as it's possible for something to be, if you catch my drift). But with a whiteboard marker (included) and a bit of graph theory (not included) you might have more luck with the mug.

We have two versions. The standard mug is a high-quality duraglaze finish and will survive over 2,000 cycles through a dishwasher before the puzzle begins to simplify itself. That's the first image above.

If you want a longer-lasting maths heirloom, we also have a bone-china option where the puzzle is encased in tricalcium phosphate and anorthite (like carbonite, only better) and fired into the mug itself. That's the second image above. It will never fade; this mug will give future alien archaeologists a puzzle to solve. However, like all bone-china, this piece of exquisite porcelain may crack under extreme temperature changes. So please do not put it in a highly elliptical orbit around the sun, or fill a chilled mug with still-boiling water.

In summary then...

Duraglaze:
Price = £14
Dishwashings ≥ 2,000
dT/dt = bring it on

Bone-china:
Price = £20
Dishwashings = ∞
dT/dt < extreme