54 | New Scientist | 25 July 2020Puzzle
set by Catriona Shearer#69 Cutting the flag
I have a stripy flag laid out on
my desk. The stripes are all of
equal width, five of them in total.
Because three of the five are
blue, I know that three-fifths of
the flag is blue. However, I take
my scissors out and make two
straight, angled cuts at both ends
of the flag, one of them at about
45 degrees, the other almost
straight across, leaving me with a
stripy trapezium. What fraction of
this trapezium is blue? Is it more,
less or the same as the three-
fifths for the original flag?Answer next week#68 Diamonds
Solution
There were no diamonds in the box.
Call the number of palaces P. There
were P2 vases and P3 diamonds, of
which Fidelio got P, leaving (P3 – P)
to share among the six daughters.
Whatever value you choose for P,
you’ll find that P3 – P is exactly
divisible by 6, so all the remaining
diamonds went to the daughters.
Why? Because it is equivalent to
P x (P+1) x (P-1), the product of
three consecutive numbers, one of
which must be divisible by 3, and at
least one of the others divisible by 2,
making the product divisible by 6.Quick
quiz #61
Answers1 The Sargasso Sea
in the Atlantic; many
details of the eels’
spawning and
migration remain
mysterious, however2 Anaphylaxis3 Japan4 The electric eel
(Electrophorus
electricus) isn’t
actually an eel, but a
knifefish; its electricity
is genuine, with
80 per cent of its
body given over to
generating it5 The many
worlds interpretation;
his father, Hugh
Everett III, originated
it in 1957Twisteddoodles
for New Scientist
Tom Gauld
for New ScientistThe back pages