Enlarge image
Photo: DER SPIEGEL
Whenever there is a visitor from England, there are always misunderstandings.
Especially times like 1:30 pm or 6:30 am cause problems for the German part of the family again and again.
Aunt Margret also likes to make fun of confusing her nieces and nephews.
“What time is it?” A niece asks her.
Margret's answer: "If you add a quarter of the time that has passed since last noon to half of the time that will pass until the next noon, you have the current time."
"Mmmmh, is that am or pm?" Asks the niece, confused.
"You'll find out," the aunt tells her.
What time was it the moment the niece asked for the time?
Two different solutions are possible as long as we calculate with English times.
The time was either
9:36 pm
- so as German indication
21:36
.
Or
7.12 am
, which corresponds to
7:12 am
.
The niece probably knows the right solution because she just got up (then it would be 7:12 a.m.) or because the sun set recently (that would mean 9:36 p.m.).
If it is 12 noon, exactly 24 hours will pass until the next noon at 12 noon.
If a is the current time in hours and a is a pm, the aunt said the following equation must apply:
a = a / 4 + (24 - a) / 2
We solve this equation for a and get:
5a = 48
a = 9 + 3/5
a = 9 h 36 min
This information matches the information provided by the aunt.
If it is 9.36 pm, a quarter of the time that has elapsed since noon corresponds to 2 hours 24 minutes.To this, we add half the time until the next noon - namely 7 hours 12 minutes - and we get 9 hours 36 minutes.
If a is an am-time, the following equation must apply:
a = (12 + a) / 4 + (12 - a) / 2
5a = 36
a = 7 + 1/5
a = 7 h 12 min
If it is 7.12 am, a quarter of the time that has passed since noon corresponds to exactly 4 hours 48 minutes.To this, we add half of the time until the next noon - i.e. 2 hours 24 minutes - and get 7 hours 12 minutes.
This puzzle comes from the English puzzle inventor Henry Dudeney, whose riddles have appeared in various magazines and books.
In his book "Amusements in Mathematics" he gives only 9.36 pm as the solution.
If you missed a puzzle from the past few weeks, here are the most recent episodes:
Pretty weird
The perfect egg
Cleverly asked
Enclosed by six circles
x, y unsolved
Floor plan with gaps
Wrong track
Seven in one go
Hundred square numbers
On the brink