17th September 2025, 01:21 pm
I recently posted the following puzzle about identical triplets.
Puzzle. Three brothers who are identical triplets live on the seventh, eighth, and ninth floors of the same apartment building. Their apartments are identical and vertically stacked. One day, all three step onto their balconies, standing in the same upright posture. The brother on the eighth floor shouts, “AAAA!” Which of the other two will hear him first?
Most readers got it right: our mouths sit lower than our ears. That means the distance from the mouth of the brother on the eighth floor to the ears of the brother on the seventh floor is shorter than the distance to the ears of the brother on the ninth floor. So the seventh-floor brother hears it first.
However, one reader, Ivan, taught me something I didn’t know: identical twins aren’t always identical. He even sent a photo of Mark and Scott Kelly — identical twins of different heights.
Of course, as a first approximation, we can assume identical triplets are identical. But mathematicians are nitpicky and like precision. Ivan (clearly a mathematician at heart) also noted that even identical twins might wear shoes with different heel heights, which could tweak the distances.
Here’s another reader submission that made me smile:
- The seventh-floor brother will hear it first, because the eighth-floor brother has fallen off the balcony and is screaming as he plummets towards the earth.
Nitpicking again: that’s a stretch, since the problem says they’re standing — but it’s still funny.
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13th September 2025, 12:47 pm
Here’s a problem from our 2025 STEP entrance test, taken by nearly a hundred students.
Problem. Pavel likes pets. All his pets except two are dogs. All his pets except two are cats. All his pets except two are parrots. The rest of the pets are cockroaches. How many pets of each kind does Pavel have?
Here is a solution from one student: one cat, one dog, and one parrot. No cockroaches—phew. Most students (and ChatGPT) found this one. By the way, I ran my whole test through ChatGPT, and this was the only mistake it made. ChatGPT, along with many students, missed the second solution: Pavel has two cockroaches.
Two more students’ answers made me smile:
- His pet cockroach is named Two. It follows that Pavel has zero cats, zero dogs, zero parrots, and one cockroach named Two.
- The parrots would eat the cockroaches, the cats would eat the parrots, and the dogs would eat the cats. Whatever he has now, he’ll be left with only dogs.
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8th September 2025, 02:58 pm
When I graduated high school, I got a special certificate I was absurdly proud of. It wasn’t about grades — students voted for these, supposedly to honor strength of character. The award was called the Pledge of Honor.
When you open it, the left-hand side has a quote attributed to Friedrich Engels: “A human is defined not only by what he does, but also by how he does it.”
I couldn’t find the official translation of this quote, so the above translation is my own. While I was searching, I found another quote: “The less you eat, drink, and read books, the less you have to shit, pee, and talk.” But I digress.
Before I explain what’s on the right-hand side of the award, a little context. I was a member of Komsomol, the Leninist Young Communist League in the Soviet Union. About 99% of students were members — not because of boundless zeal, but because not joining could hurt your chances of getting into college or landing a job. Back in high school, I was brainwashed into believing that the Komsomol was trying to do good, so I signed up as soon as I was eligible — I wasn’t thinking then about colleges or jobs.
Now I am ready to translate the right-hand side, which said: “The Komsomol organization of Moscow School No. 444 PLEDGES ON ITS HONOR that Tanya Khovanova will never, ever, anywhere disgrace the high calling of a Komsomol member.”
I lost my rose-colored glasses right after high school. How that happened is another story, but let’s just say the “never, ever” promise had a shelf life of about a month.
There was another, more prestigious certificate called the Torch-Carrier of Communism. Two students in my class received this honor. One of the torches soon moved to Israel.
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