The Three Utilities Problem

https://commons.wikimedia.org/wiki/File:3_utilities_problem_blank.svg
Image: Wikimedia Commons

Each of three houses must receive water, gas, and electricity. Is it possible to arrange the connections so that no lines cross?

No, it ain’t. Remove one house and draw connections to the other two:

https://commons.wikimedia.org/wiki/File:3_utilities_problem_proof.svg
Image: Wikimedia Commons

This divides the plane into three regions, here colored red, yellow, and blue. Placing the third house into any of these regions denies it access to the correspondingly colored utility. So the task is impossible.

Pleasingly, the task can be accomplished on a Möbius strip:

https://commons.wikimedia.org/wiki/File:3_utilities_problem_moebius.svg
Image: Wikimedia Commons

And a torus can accommodate up to four houses and four utilities:

https://commons.wikimedia.org/wiki/File:4_utilities_problem_torus.svg
Image: Wikimedia Commons

(By Wikimedia user CMG Lee.)

08/31/2025 UPDATE: Reader Guy Bolton King points out that Mathsgear sells a mug embossed with the puzzle. The joke here is that this makes the puzzle solvable — like the torus, the mug is of topological genus 1, “a blob with 1 hole in it,” so it admits the same solution.

And reader Shane Speck writes, “My sneaky solution … has always hinged on the fact that in reality, houses don’t all have separate pipes, and popping on a shared water pipe instantly reduces the problem to the status of incredibly trivial”:

shane speck utilities solution

“The problem doesn’t, after all, say you can’t do that… :)”

(Thanks, Guy and Shane.)

| Puzzles

Commemoration

Working in the Indian Medical Service in 1897, British physician Ronald Ross discovered a malarial parasite in the gastrointestinal tract of a mosquito, proving that these insects transmitted the disease. He sent a poem to his wife that’s now inscribed on a monument in Kolkata:

https://commons.wikimedia.org/wiki/File:Plaque_(1)_of_Ronald_Ross_Memorial,_Kolkata.jpg
Image: Wikimedia Commons

He won the Nobel Prize for Physiology or Medicine in 1902, the first British Nobel laureate.

| Science & Math

Olbers’ Paradox

https://pixabay.com/en/natural-starry-sky-night-view-2065714/

Why is the night sky dark? If the universe is static and infinitely old, with an infinite number of stars distributed homogeneously in an infinitely large space, then, whatever direction we look in the night sky, our line of sight should end at a star. The sky should be filled with light.

This puzzle is most often associated with the German astronomer Heinrich Wilhelm Olbers, but Edgar Allan Poe made a strikingly similar observation in his 1848 prose poem Eureka:

Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy — since there could be absolutely no point, in all that background, at which would not exist a star.

Poe suggested that the universe isn’t infinitely old: “The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all.” We now know that the sky is dark because the universe is expanding, which increases the wavelength of visible light until it appears dark to our eyes.

| Science & Math

“Hence These Rimes”

Tho’ my verse is exact,
Tho’ it flawlessly flows,
As a matter of fact
I would rather write prose.

While my harp is in tune,
And I sing like the birds,
I would really as soon
Write in straightaway words.

Tho’ my songs are as sweet
As Apollo e’er piped,
And my lines are as neat
As have ever been typed,

I would rather write prose —
I prefer it to rime;
It’s less hard to compose,
And it takes me less time.

“Well, if that be the case,”
You are moved to inquire,
“Why appropriate space
For extolling your lyre?”

I can only reply
That this form I elect
‘Cause it pleases the eye,
And I like the effect.

— Bert Leston Taylor

| Poems

On the Nose

https://commons.wikimedia.org/wiki/File:Carvone.svg

The distinctive smells of spearmint and of caraway seeds are produced by mirror images of the same molecule, carvone.

The fact that we can distinguish these smells shows that our olfactory receptors can sometimes discern the “handedness” of such molecules. But this isn’t the case with every set of “enantiomers.”

| Science & Math

Wayfarer

https://commons.wikimedia.org/wiki/File:Francesco_Segala_maze.png

Francesco Segala (1535-1592) made his name as a sculptor in Padua, but he’s remembered as a father of the picture maze.

Make your way from the traveler’s cup to the exit at bottom center.

| Puzzles