New Scientist - USA (2021-12-18)

The back pages Puzzle answers

#144 Shaken, not stirred

Solution

There is a trap to avoid here, as a 6:1 gin to

vermouth ratio feels like it should be halfway

between 5:1 and 7:1, but Grace tried mixing

equal quantities and it tasted wrong.

The two bottles are 5/6 gin and 7/8 gin,

respectively, and Grace wants a mixture that is

6/7 gin. That means 300 millilitres of the first

bottle would have 250ml gin and 50ml

vermouth, and 400ml of the second bottle

would have 350ml gin and 50ml vermouth,

which when mixed together gives 700ml of

martini in Grace’s perfect 6:1 ratio. Cheers!

#145 Up the sprout

Solution

The sprouts weigh 0.8 kilograms so I owe 80p.

The scales are experiencing 0.8kg weight from

the sprouts and a balancing 0.8kg from the

tension in the string that is attached to the floor.

If you don’t believe this answer, set up a pulley

and a scale and test this out for yourself.

#146 Meg’s pegs

Solution

Meg’s code must be yellow-yellow-yellow-yellow.

The only way that Greg can be certain of Meg’s

code is if Meg says Greg had zero correct colours.

For any other combination of correct colours and

positions, there are at least two possible codes.

#147 Lebkuchen race

Solution

The ant walking the length of the packet won the

race, because its journey was slightly shorter than

that of the ant walking around the circumference

of the packet’s end.

If we call the diameter of a biscuit D, then the

length of the packet is 15 x D/5 = 3D, while the

circumference is πD = 3.14 D.

Quiz of the year

Answers

1 B – Caffeine

2 C – Posture-correcting stairs

3 B – The Chicxulub asteroid impact

4 D – They can vibrate to cancel out

other frogs’ calls

5 D – 540 kilometres per hour

6 B – The Borg

7 D – 7

8 A – Pembrokeshire

9  B – Capsaicin

10  C – Hexadecanal

11 D – They eat each other’s wings

12 A – El Salvador

13 B – Sharks

14 B – 200,000 to 2 million

15  C – 375

16  D – Helping cats show us affection

17 C – Russia

18 B – Davemaoite

19 A – Mansfield Park

20 C – Hell heron

21 D – Two sea scorpions mating

22 D – 500,000

23  C – A slab avalanche

24 A – Nickel

How did you do?

18-24 Is that a stack of New Scientists

we see beside you? Bravo! You clearly

know your sciencey stuff.

12-17 The unmistakable whiff of

knowledge is emanating from you.

Congratulations.

6-11 Hmm. Feels like a heady

combination of luck and educated

guesses. Still, it is the taking part that

counts, so well done.

0-5 Oops. Even guessing every time

would have delivered six points, on

average. Perhaps you require a New

Scientist subscription in 2022!

Cryptic crossword #72

(set on 11 December)

Answers

ACROSS 1 Stopcock, 5 Swab, 9 Pizza,

10 Spoke of, 11 Seethe, 12 Pupal,

14  Retort, 15 Pepsin, 18 Sisal,

20  Lurked, 22 Dungeon, 23 Dents,

24  Down, 25  Theremin

DOWN 1 Saps, 2 Ooziest, 3  Chanterelles,

4 Cashew, 6 Whelp, 7  Baffling, 8 Doppler

radar, 13  Presided, 16 Sternum,

17  Flinch, 19 Sinew, 21  ISBN

#143 X marks the Spot

(set on 11 December)

Solution

The patio requires 196 white tiles

and 29 black tiles. Here’s why:

Suppose the patio is a k × k square

containing a total of k2 tiles. If k is odd we

need 2k – 1 black tiles and so k2 – 2k + 1

= (k – 1)2 white tiles (a square number);

and if k is even, (k – 1)2 – 1 (which is one

less than a square). But no permutation

of 1, 6 and 9 is one less than a square; so

we are looking for a square for which k-1

is even. Of the three squares 169, 196

and 961 only 196 = 142 is even; so

(k – 1)2 = 196 = 142 and k = 15. We

need 2k - 1 = (2)(15) – 1 = 29 black

tiles and 196 white tiles to make a

15 × 15 square.

86 | New Scientist | 18/25 December 2021

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