MAGIC MATHS
The Knockout Competition
Henry asked his teacher if he and the
other boys in class 5 could have a
penalty kicks competition, which they
would play at lunchtime in their nearby
sports ground.
Luckily, there were exactly 16 boys in the
class and they all wanted to take part in
the competition. So each boy wrote his
name on a slip of paper and put it in
Miss Smith’s woolly hat. Each pair of
boys drawn would be goal-kicker and
goalkeeper in turn, and each kicker
would get 6 shots.
All 16 boys would play in the first round,
the 8 winners would play the second
round, then there would be the semi-
final and the exciting final, when the
winner would get a special certificate
from Miss Smith, which would be
displayed on the classroom wall.
But guess what! There were 7 girls in the
class who also wanted to take part in the
competition. They said it wasn’t fair to
have a competition just for the boys and
Miss Smith agreed.
There were now 23 competitors. How
can you do a knockout competition with
23 people? Miss Smith explained that:
JOKES
Knock, Knock.
Who’s There?
Abyssinia.
Abyssinia who?
Abyssinia when I get back!
From Thea
4 = 2 × 2 = 2 2
8 = 2 × 2 × 2 = 2 3
16 = 2 × 2 × 2 x 2 = 2 4
and all these numbers are perfect for
arranging knockout competitions.
But people don’t put their names on
competition lists in neat, convenient
powers of 2.
So for any knockout competition, you
need to subtract the number you have
from the next power of 2, in this case 2 5
or 2 × 2 × 2 × 2 × 2 = 32.
32 – 23 = 9, so 9 lucky players get a bye
into the second round – meaning that
nine of the children will automatically go
into round 2.
The other 14 (23 – 9) competitors play
the first round. The 7 winners of this
round join the 9 byes. Then the 16 play
the second round, and the competition
progresses as before.
In case any of the girls backed out when they realised how good the boys were,
Henry made a table:
Number of competitors Number of byes Number in round 1
17 15 2
18 14 4
19 13 6
20 12 8
21 11 10
22 10 12
23 9 14
PS The proud winner, whose certificate is displayed on the classroom wall, was
Tabitha Messi-Brown. But with a name like that the others didn’t really stand a
chance, did they!
What is a fisherman’s favourite instrument?
A cast-a-net!
Isabelle D, 11¼
Knock Knock!
Who’s there?
Tish.
Tish who?
Oh please don’t
sneeze on me!
Nya H, age 8
Why was the tractor magic?
Because it drove down the road and turned into a field!
From Ellie, age 12
Alex and Alan took their
lunches to the local café
to eat.
‘Hey!’ shouted the
manager. ‘You can’t eat
your own food in here!’
‘Okay’ said Alex. So he
and Alan swapped their
sandwiches.
From Lottie
Book titles
Plants by Tom Atoe
The Toilet by Sue Age
Wild Boars by Ima Hogg
From Rowan M
Japanese Cuisine by Sue Shee
From Joseph Cook, age 11
Why can’t Dalmatians hide?
Because they’re always spotted!
Why don’t seagulls live in the bay?
Because otherwise they would be called
bagels!
From Rowan M, age 10
NEXT MONTH IN AQUILA :
MATHS IN NATURE
JOIN US ON AN INVESTIGATIVE JOURNEY FULL OF WONDER AND SUNFLOWERS
(AND SLIME MOULD). THAT’S RIGHT, MAY’S ISSUE IS ALL ABOUT . . .
l MEET EUCLID OF ALEXANDRIA; GREEK MATHEMATICIAN AND FATHER OF GEOMETRY. HE HAS A CRATER ON THE MOON NAMED AFTER HIM - HOW’S
THAT FOR MATHS IN NATURE?
l COME WITH US ON A NUMBERS HUNT WITH FANATICAL FIBONACCI (THIS ONE COMES WITH A WARNING THOUGH, READERS MAY BECOME PERILOUSLY
OBSESSED WITH SPIRALS, ED).
l OUR PENS SENSE AND HELPS EVERYONE EXPERT, KATE DANIELS, IS FINDING OUT ALL ABOUT BANTER.
l HARVEY’S GIVING OUT GOOD VIBRATIONS (SEE WHAT I DID THERE?) WITH SENSATIONAL SOUND SCIENCE.
l AND, LAST BUT NOT LEAST, WE’VE DISSECTED OWL PELLETS LOOKING FOR RAT SKULLS, WE’VE CONDUCTED TUMMY TURNING DIGESTION EXPERIMENTS
AND DONE UNSPEAKABLE THINGS WITH CHEESY CRISPS BUT I THINK THIS MUST BE THE MOST DISGUSTING AND FASCINATING SCIENCE PROJECT
WE’VE EVER EMBARKED UPON: E.B. IS GETTING UP CLOSE AND PERSONAL WITH SOME MAZE-SOLVING MANY-HEADED SLIME MOULD!