The Guardian - UK (2022-04-30)

• The Guardian Saturday 30 April 2022

66

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 16,218

123 4567

89

10 11

12 13 14

15 16

17 18 19 20

21 22

23 24

Across
1 Legal (6)
4 Refuge (6)
8 Assessed (5)
9 Derisive (7)
10 Happening now (7)
11 City of northern Italy, with a
university established in 1222 (5)
12 Demolished (9)
17 Quick look (informal) (5)
19 Lacking profundity (7)
21 Incessant (7)
22 Former PM (5)
23 Flung (6)
24 Hold gently and protectively (6)

Down

1 Words of a song (6)

2 Irrigated (7)

3 Excessive (5)

5 Income when one is ill (4,3)

6 Scottish landowner (5)

7 Offi cial language (and a native) of

Hungary (6)

9 Car drivers (9)

13 Expression of amazement (5,2)

14 Shoulder muscle (7)

15 Approach (6)

16 Momentary pain (6)

18 Praise — honour (5)

20 Fossil resin used for jewellery (5)

Solution No 16,217

GRANDS LAM

AWE S UAO

B L A I R SHANNON

OLA I LDT

LIKENESS LISP

IIITZNA

TONGUE S I NGER

I GMFMSN

OXON C I ABATTA

NNMAAAS

ITALICS BOGUS

SISCWEE

TURNSTONE

1 Enormity refers to the

outrageousness of a barbarous or

wicked act; enormousness to the

hugeness of something. Fulsome

means “repulsively unctuous and

probably insincere”.

2 In a) Candy suggests equating

the expression to √p - √q. [Why

the minus sign?] The expression is

positive; so p > q. Squaring: 1/(3 +

√8) = p + q - 2√(pq). Multiply top and

bottom of fraction by (3 - √8); we

get p + q = 3 and pq = 2; so (p – 2)(p -

1) = 0; now p > q , so p = 2, q = 1; and

the answer is √2 – 1. [Now check by

squaring!]

b) Put a = - (b + c) in the expression

and it vanishes; so we are right

to suspect a + b + c is a factor. On

performing the long division we

fi nd (a + b + c)(a2 – a(b + c) + (b2 – bc

+ c2). Check by re-multiplying!

Point to Ponder: Why is the

quotient longer than the dividend?

3 We need a little construction.

[Point to Ponder: How do we

know when such an addition

is necessary?] Draw in BC, so

connecting each of A , B, C & T to

each and every other one. Also:

<BAC = <BCT!

[“The angle

between a chord

and a tangent

through one of

the chord’s ends equals the angle

in the alternate segment.”] Also

<BTC = <ATC (shared angle); so

triangles BT’C’ & CTA are similar.

[The fi rst is fl ipped to make the

correspondences clearer. T & T’ are

the same point named for diff erent

triangles, as are C & C’.] The chord

and tangent meet on the circle if,

eg, B and C coincide.

Alternatively, AC could

be perpendicular to

AB. Then they don’t

meet. AT/CT = C’T’/BT’

-> AT.BT = (CT)2. Also:

AT = (AB + BT); so (AB

+ BT)BT = (CT)2. Point to Ponder:

Can we fi nd AC?

4 20 cm away. [Point to Ponder:

Why?]

5 “TEN” would do. (Any other

answers?)

Wordplay: Wordpool a), d), b);

Jumblies PREVARICATION;

Dropouts INDULGE; End of the

word EXPIRY; Cryptic SCOOTER,

STAR PUPIL, LETHARGIC; Missing

Links a) rent/strike/rate b) pig/sty/

list c) chicken/feed/back d) cheap/

skate/board e) comic/turn/coat

f ) car/go/west

C

B

AT

C’ T’

A T,T’

C,C’

B