New Scientist - USA (2020-07-18)

(Antfer) #1
54 | New Scientist | 18 July 2020

Puzzle
set by Rob Eastaway

#68 Diamonds
“Once upon a time,” began Ivan
the storyteller, with children at his
feet, “there lived a queen called
Factoria who had six daughters
and many palaces. In each palace,
she kept as many crystal vases
as she had palaces, and in each
vase were as many diamonds as
there were vases in that palace.
Then one day the Queen died,
leaving a will: ‘I leave one vase
of diamonds to my loyal servant
Fidelio. The rest of the diamonds
I will share equally between
my daughters. Any remaining
diamonds, Fidelio will put in
this box.’”
Ivan reached into his pocket and
pulled out a small wooden casket.
“And this is the box!”
“How many diamonds are there?”
screamed the children.
“If you can tell me, I will give you
the box,” said Ivan.
“But you haven’t told us how
many palaces...” they cried.
Ivan winked.

How many diamonds are in the
box? How can you be certain?

Answer next week

#67 My prime


Solution
“My prime” could be 23, 43, 67
or 89, but whichever it is, the two
digits must differ by 1.
You could discover this by trial and
error, but there is a short cut. Let us
call the number’s larger digit “a”
and the smaller “b”. The difference
between their two squares is a² - b²,
which is the same as (a + b) x (a – b).
However, we were told this
difference is a prime number, so the
only two factors of ab are itself and


  1. Therefore a + b must be the prime
    itself, while a – b, the difference
    between the digits, is equal to 1.


Quick
quiz #60
Answers

1 One or other of
your shoulder blades

2 Stoichiometry

3 The Sky at Night.
The International
Astronomical
Association
bestowed the
honour on Patrick
Moore’s astronomy
programme on its
50th anniversary
in 2007

4 Srinivasa
Ramanujan

5 A surface-active
agent, or surfactant

Twisteddoodles


for New Scientist


Tom Gauld
for New Scientist

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