This old gag caught my eye recently:
As usual in these cases, it’s a trick question.
Turns out it resolves fairly simply when we just “follow the money”.
Start with the $300 being tendered. The desk clerk later refunds $50 and keeps $250 for the room. Of that $50, each friend gets $10 while the bellhop keeps $20. So the final distribution of funds is:
- Hotel: $250
- Bellhop: $20
- Three Friends: $30 ($10 each)
For a total of $300, just as we’d expect.
The misdirection is pointing to the $90 each friend paid ($270 total) and considering that the same category as the $20 taken by the bellhop. Two different things (and the $250 for the room isn’t even in the equation).
Instead, as in the bullet list above, consider the $250 held by the hotel, the $20 held by the bellhop, and the $30 held by the friends. When we consider things all in the same category, the math works out.
But that’s hardly surprising.
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Another way to look at it: The friends end up paying $270 — an overpayment of $20 for the $250 room. That extra $20 is in the hands of the bellhop.
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If this tickled your interest, here’s more Fun with Numbers.
Stay numeric, my friends! Go forth and spread beauty and light.
∇
October 22nd, 2026 at 2:44 pm
It may be an oldie, but it’s a new thing if you’ve never seen it before.
And hence one of my all-time favorite xkcd cartoons: Ten Thousand.
As the cartoon’s hover gag says: Saying “what kind of an idiot doesn’t know about the Yellowstone supervolcano” is so much more boring than telling someone about the Yellowstone supervolcano for the first time.
October 22nd, 2026 at 3:45 pm
Yep, numbers are NOT immutable. Being in the land survey business has shown me things about numbers that boggle my mind. Once you start getting more than 3 numbers, you can do things with them people never even thought of 😀
I like the assumptions made in the joke, ie, that all math is the same, hahahhaa.
October 22nd, 2026 at 4:52 pm
I grok what you’re saying, but “immutable” might not be the best word for it. Part of the beauty of math is how well defined it is. The value of pi, for example, is fixed by the geometry of reality.
That said, the mapping between math and language is mutable, indeed. This is a word problem that depends on a deceptive description to mislead the reader. When expressed as actual math, it would be a lot harder to hide the trick. Which is different from other math gags that depend on a tricky illegal operation — one most wouldn’t recognise — to prove something silly, such as 1=2 or 2=0 [see this post if interested in such tricks].
(Hmmm… I should work out the actual math for this hotel room gag… something like:
Nothing missing! 😁
October 22nd, 2026 at 4:45 pm
I remember being stymied by this one many years ago, but for some reason, this time, the fact that the $20 was being applied in the wrong direction in the second to last paragraph just jumped out. It should be subtracted from the $270 as overpayment to get to the $250 figure. If we want to get to the $300 figure, we need to add the original overpayment amounts ($30 + $20) to the correct amount ($250).
I’m unreasonably proud of myself for catching it this time before the explanation.
October 22nd, 2026 at 4:57 pm
And rightfully so. That’s what makes us old farts so valuable: years of experience! 👨🏼🦳
November 3rd, 2026 at 11:14 am
I like trick questions too: https://noghostnomachine.wordpress.com/2024/04/04/trick-questions/
I also like the trick questions that go under the name “philosophy”. As in, most of philosophy.
November 3rd, 2026 at 11:38 am
Ouch! The first one goes over my head. Why wouldn’t the object move in the NNE direction?
The second one seems an “it depends” question for biologists. My uninformed wild guess is that some egg-laying proto-chicken laid an egg with a mutation to actual-chicken. (Indeed, per your hint.)
The third one … I don’t do statistics! Ugh, blech, yuck!! 😆
Philosophy can be fun, but in my cynical curmudgeon-y old age I’ve concluded that Sturgeon’s Law is especially acute with regard to philosophy. I think the fraction of it that is good, is very good, but there seems a great deal of pointless chaff to me. And too many endless rabbit holes and dumb notions. But then, I’m a known philistine. 🤷🏼♂️
November 3rd, 2026 at 2:18 pm
The pushers are unable to see the underlying structure. Their burden is actually a rail car on an east-west track. When it yields, it will go east.
November 3rd, 2026 at 5:00 pm
Ah, it’s a riddle. I can never figure those out. 😔 I need all the information.