Non-Identical Identical Triplets
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.
Share:
Osmin:
Nice one, always nice to read you!
18 September 2025, 6:13 amI would however argue that this is an example of puzzle where the expected answer is certainly a bit further from the reality than the answers that take physical factors into account (especially the shape of the building/balconies, but also wind etc…) So, in a sense, the way you describe the answers of the readers and of your students (“wrong/right reasons”) might be a bit too definitive? For the students this could induce a bias toward a unique way of thinking (which might actually be the goal?)
Moreover, to be really precise, you should also include in the puzzle that “all three step onto the same point of their balconies”. Except if they have very small balconies (smaller that their mouth-ear distance), this could also influence your answer 😉
Ted:
I suppose you could insist that when you said “identical” you were refering to their physical attributes, not their genetics.
20 September 2025, 11:14 pm