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?
I gave this puzzle to my students, and two of them offered the right answer for the wrong reasons. One said, “The seventh-floor brother, because air is warmer closer to the ground and sound travels faster in warmer air.” Another said, “The seventh-floor brother, because the air is denser at lower altitude and sound travels faster in denser air.”
What is the right reason?
Share:
Oscar Cunningham:
Because people’s mouths are lower than their ears on their heads?
26 August 2025, 12:23 pmDan:
The seventh-floor brother’s ears are closer to the eighth-floor brother’s mouth (than the ninth-floor brother’s ears are).
26 August 2025, 12:41 pmLiviu:
The position of the mouth 🙂
26 August 2025, 2:16 pmKonstantin:
a person’s ears are above mouth
26 August 2025, 3:09 pmAlois:
mouth ear distance to sevnth floor is shorter
26 August 2025, 4:15 pmShawn:
The 7th because the 8th had fallen off of the balcony and is screaming as they plummet towards the earth?
26 August 2025, 8:21 pmIvan:
The ear-mouth-distance argument does not hold, since the identical twins do not necessarily share the same height* or taste (they could choose shoes with different heel hight). The fact that the brothers are on their balconies, standing in the same upright posture invalidates Shawn’s reasoning (but I like his sense of humour).
* see a picture ot some different-height identical twins:
27 August 2025, 4:07 amhttps://en.wikipedia.org/wiki/Twin#/media/File:Mark_and_Scott_Kelly_at_the_Johnson_Space_Center,_Houston_Texas.jpg
Ted:
The ninth is the highest floor of the building. It’s balcony has no roof to reflect the sound down to its occupant?
1 September 2025, 7:12 pmTanya Khovanova's Math Blog » Blog Archive » Non-Identical Identical Triplets:
[…] I recently posted the following puzzle about identical triplets. […]
17 September 2025, 1:22 pm