The Guardian - 07.09.2019

Section:GDN 1N PaGe:62 Edition Date:190907 Edition:01 Zone: Sent at 6/9/2019 16:11 cYanmaGentaYellowbl

• The Guardian Saturday 7 September 2019

62

Puzzles

Ye ste r d ay ’s

Quick crossword

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Chris Maslanka

Solutions

Sandwich sudoku

Medium

Place the digits

from 1-9 in each

row, column and

3x3 block.

The clues outside

the grid show

the sum of the

numbers placed

between the 1 and

9 in that row or

column.

Quick crossword no 15,393

1234567

89

10 11

12

13 14 15

16

17 18 19

20

21 22 23

24

Across

1 Person experienced in life (3,2,3,5)

8 Vandal (7)

9 Comes closer to (5)

10 Team up (with) (4)

11 Day of very hot and sunny

weather (8)

13 Completely saturated (6)

14 Wood cut and prepared as

building material (6)

17 Discursive (8)

19 Badly behaved child (4)

21 Machine that produces the winning

Premium Bond numbers (5)

22 Blood disorder — ie I am Ana (anag)

(7)

24 Get married? (4,3,6)

Down

1 Cut the grass (3)

2 Irritated (7)

3 Bogus (4)

4 Roman lyric poet, d.8BC —

a chore (anag) (6)

5 Inspiring a feeling of delight (8)

6 Limits within which something

can be eff ective (5)

7 Member of the British 7th

Armoured Division in North

Africa, 1941-2 (6,3)

10 Able to soak up liquid easily (9)

12 Determined to achieve something

at all costs (4-4)

15 Female star of the 1942 fi lm

Casablanca, d.1982 (7)

16 Provoke to fury (6)

18 Capital of Belarus (5)

20 Welcome — precipitation (4)

23 Chopper (3)

Solution no 15,392

KDLP

MA L I C I OU S

FNNNR I

SLOG GANGRENE

EAHE C

STOREY T INPOT

CO EG

THRONG SUP I NE

ERMOI

BREAKAGE T I TS

SWT L I O

FRUI TLESS

YSYM

Pyrgic: 1 Radio 4 is a great source of

linguistic and treasurable solecisms,

either of their own making, or punted

on from contributors. This one comes

from the redoubtable Woman’s Hour

but it is heard everywhere: I didn’t

think it was manly behaviour on

his behalf. It should be on his part ,

as I’m sure you all yelled at your

radios. Thanks to Linnet McMahon

(Wantage) for sending this in.

2 There were originally 64 in the

posse. Then 25 rolled up. They each

received 46 candies. As a warm-up

case, consider the case when 4 at

fi rst turned up and Marshal bought

16 candies. He kept 2 and had 14 to

share. 14 = 1 × 14 or 2 × 7. They might

have got 1 sweet each (unlikely) or 2

sweets each; in the latter case there

were 7 riders in all and 3 rolled up. In

the harder case consider the squares

between 4 & 100: 9, 16, 25, 36, 49,

64. The corresponding numbers for
    sharing after Marshal has taken 2
    are: 79 (prime); 254 = 2 × 127; 623 = 7
    × 89; 1294 = 2 × 647; 2399; 4094 = 2
    × 23 × 89; 6599 (all reduced to prime
    factors). The only one having a factor
    between the original posse number
    and twice that is: 64; 64 2 − 2 = 4094
    = 2 × 23 × 89; and this factor is 89; so
    25 turned up and each of the riders
    received 46 sweets. I am grateful to
    Jon Chapman for pointing out this
    puzzle can be set and solved with
    even less information.
    3 First she gave it a name: S, then
    replaced x 2 by y, doubled everything
    and added 1 to get: 2S + 1 = 1 + 2y + 3y 2

• 4y 3 + 5y 4 + ... The right-hand side as
  1/(1 − y) 2, which is 1/(1 − x 2) 2; so S may
  now be easily found. Point to Ponder :
  When does the series converge?

4 The fl ea can only have arrived at

the nth step from the (n − 2)nd [with

2 steps] or from the (n − 1)st [with

1 step]. If the number of ways of

arriving at the nth be u[n], then u[n]

= u[n − 1] + u[n − 2]: the condition

for a Fibonacci series. The equation

between terms is called a recurrence

relation. We can solve this, or lazily

consider the fi rst two steps. u[1] =

1; u[2] = 2; so the sequence is 1, 2, 3,

5, 8... Point to Ponder : Can you fi nd

an expression for u[n]? Wordpool

a), d), c); EPU PARENTHETICAL;

Brant Ub SUPERSEDE; SEDENTARY

& SEDER; Tom Swifties SLYLY;

Cryptic MASTODON, FLUSHING

MEADOWS, INTESTATE; Missing

Links a) soft/landing/gear; b) fi nal/

score/board; c) hand/clap/trap; d)

soft/power/broker; e) hard/rain/

water; f ) table/top/dog.

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