52 | New Scientist | 23 November 2019
The back pages Puzzles
Cryptic crossword #19 Set by Wingding Puzzle set by David Bodycombe
#31 Three hats
Ariana, Beverley and Cassie are standing
in a line. They know that two of them are
wearing black hats and one is wearing a white
hat – or vice versa – in an arrangement like
the one shown above.
Beverley and Cassie can see the hats in
front of them but not behind, while Ariana
can’t see any hats. They can only say “white”
or “black” to announce their own hat colour.
Who will be able to confidently state their
hat’s colour first? And who will be second?Answer next week#30 Sticking in a PIN
Solution
We are looking for a four-digit PIN containing
a zero that, when squared, ends in itself.
This is known as an “automorphic” number.
A quick mental calculation confirms that, of
the numbers 0 to 9, only 0, 1, 5 and 6 end in
themselves when squared, so our number must
end with one of these. Moving on to two-digit
numbers, you will find that only 00, 01, 25 and
76 end in themselves when squared.
There are algebraic ways of deducing the digits
of longer numbers, but trial and error can be
just as quick. Automorphic numbers ending with
0 or 1 always end with 0000 or 0001 when
squared, which rules them out.The only “proper” four digit number that,
when squared, ends in itself is 9376, which
makes 87909376.However, 9376 doesn’t contain a zero.
Fortunately, PINs can have leading zeroes.
The only number that has the required property
is 0625 (its square is 390625), so this must be
the answer.Quick Crossword #45 Answers
ACROSS 8 Hemi, 9 Leopard cat, 10 Tensor, 11 Flamingo, 12 RGBA, 13 Semidesert, 16 Anne, 17 Unbox,
18 SASH, 19 Esaki diode, 21 Erie, 22 Elon Musk, 26 Lactic, 27 Homosphere, 28 AloeDOWN 1 Jet engines, 2 Oil shale, 3 Ultrasound, 4 Roof, 5 NASA, 6 Eddies, 7 Yang, 14 Dixie flyer, 15 Russia Iron,
18 Seed coat, 20 King of, 23 Lyot, 24 USPO, 25 Knee ACROSS
1 Youth Climate
Leaders fall out of
vehicle in an instant (5)
3 Powerful DNA: I’m
not sick (8)
9 Liberal Tory hid
growth stimulator (7)
10 About a way to sleep (4)
11 Some walrus tastes like
iron oxide (4)12 The French chase male
insect under the ground (6)
14 Break up carbon and
drink digestive fluid,
one’s forgotten (7)
16 Stick poster in this place (6)
19 Form of energy with
little mass (5)
21 Move swiftly around
new quartz (5)24 Trade union stands by
automaton, having lost
zero fish (6)
25 Occupation for one
absorbed by scientific
instrument (6)
26 Speeding around central
Amman, causing damage (7)
27 Make garment, taking in
bottom of hem, for duck (4)Editor’s note: Unfortunately, due
to radiation exposure, mutations
have occurred in 14 of the
solutions in this crossword.
In these cases, the word that
should be written into the grid
is a real word, but it is one letter
different to the word described
by the clue. There are three types
of mutation: (a) the addition of
A, T, G or C; (b) the deletion of
A, T, G or C; (c) the substitution
of A, T, G or C for one of the other
three letters.
The numbers in brackets
indicate the length of the word
that is clued, which may be
different to the length of the
word written in the grid.The quiz will be back next week, as well as the next quick
crossword and the solution to this cryptic crossword.DOWN
1 Conservative supports
timetable for turning (8)
2 South American mammal
said to resemble fish
faeces (5)
4 Poet essentially made
mess of swelling (6)
5 Incorporated into brown
food container (3,3)
6 Pigmented areasperiodically carried
on leader (7)
7 Water birds gutted to
get places to sleep (4)
8 Ethical eel with tail cut
off by line (5)
13 Primarily horticultural
boundary line (8)
15 Note in Blondie song –
it’s infectious (7)17 Iron got into German
court – the result of a
mutation? (6)
18 Shocked at men’s
reproductive organ (6)
20 Upland lifted to
make space (4)
22 Bone in leg injured under
muscle initially (5)
23 Notice part of the ear (4)Get in touch
Email us at
[email protected]
[email protected]ABC