New Scientist - USA (2020-07-18)

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

The back pages