NO
1
IN A SERIES OF SIX
This problem looks
complicated but
req uires only a few
simple techniq ues to
reveal a remarkable
solution and a 2500
year old theorem.
le at A.
g
n
a
t
h
ig
r
a
s
ha
Triangle ABC
BC as
d
n
a
C
A
,
A
B
n with
w
a
r
d
e
r
a
s
le
c
Semi-cir
own.
h
s
s
a
s
r
e
t
e
m
dia
n the
w
o
d
e
it
r
w
,
0
d BC = 1
n
a
8
=
C
A
t
a
h
ed area.
d
a
Given t
h
s
l
a
t
o
t
e
ird of th
h
t
e
n
o
f
o
e
lu
va
T/FMSP)
allenge (UKM
h
C
cs
ti
a
m
e
am Math
From Senior Te
Further Mathematics Support Programme
The FMSP works with students and teachers to promote, enrich and support
mathematics in schools and colleges. For more information visit our website:
Scan the QR
code to check the
solution and find
other problems.
www.furthermaths.org.uk
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NO
2
IN A SERIES OF SIX
The first part can be
solved with decimals
and percentages. It
leads on to exploring
a seq uence of
numbers with powers
and using logarithms
for solving eq uations.
ht that
ig
e
h
a
o
t
p
u
s
d bounce
n
a
d
e
p
p
o
r
opped. It
d
r
d
s
a
w
it
A ball is
h
ic
from wh
t
h
ig
e
h
e
h
t that is
t
h
f
ig
e
h
a
o
is 75% o
t
e
each tim
,
e
c
n
u
o
b
o
t
s
continue
eight.
h
s
u
io
v
e
r
p
e
h
75% of t
it bounces
e
r
o
f
e
b
e
k
a
does it m
s
e
c
n
u
o
b
y
n
ight?
e
h
l
a
How ma
in
ig
r
o
e
10% of th
n
a
h
t
s
s
le
o
t
up
n 1%?
a
h
t
s
s
le
r
o
f
y
How man
Further Mathematics Support Programme
The FMSP works with students and teachers to promote, enrich and support
mathematics in schools and colleges. For more information visit our website:
Scan the QR
code to check the
solution and find
other problems.
www.furthermaths.org.uk
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NO
3
IN A SERIES OF SIX
This problem is easy
for anyone to start
but gets increasingly
complicated and
req uires a proof to
know you have the
best answer.
dded,
a
e
r
a
s
r
e
g
e
t
ber 2, in
m
u
n
e
h
t
h
it
joined if
e
r
a
s
Starting w
r
e
b
m
u
any two n
t
a
h
t
o
s
r,
e diagram
e
h
d
r
T
r.
e
in o
h
t
o
e
h
t
factor of
a
is
m
e
h
t
s 2 to 6.
f
r
o
e
b
m
one
u
n
e
h
t
ctions for
e
n
n
o
c
e
h
t
s
show
hat can be
t
r
e
b
m
u
n
m
aximu
rs are
e
b
m
u
What is the m
n
o
w
t
s joining
e
n
li
o
n
if
d
e
reach
oss?
allowed to cr
ICH
blem from NR
Based on a pro
Further Mathematics Support Programme
The FMSP works with students and teachers to promote, enrich and support
mathematics in schools and colleges. For more information visit our website:
Scan the QR
code to check the
solution and find
other problems.
www.furthermaths.org.uk
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NO
4
IN A SERIES OF SIX
It’s amazing that the
height of the crossing
can be calculated at
all in this problem,
surely it is necessary
to know how far apart
the two ground level
stations are?
400m
600m
?
the
in
n
w
o
h
s
e
r
a
ble cars
a
c
r
o
f
s
e
ir
w
600m
t
f
o
t
h
ig
e
h
l
a
Two straigh
es a vertic
h
c
a
e
r
r
a
c
wn.
e
o
n
h
s
O
.
s
a
m
a
m
r
0
g
0
ia
4
d
height of
l
a
ic
t
r
e
v
a
r
e
and the oth
ross?
c
s
e
ir
w
e
h
t
o
ht d
At what heig
art
es by Ian Stew
ti
si
o
ri
u
C
l
ca
ti
athema
's Cabinet of M
rt
a
w
e
St
r
o
ss
From Profe
Further Mathematics Support Programme
The FMSP works with students and teachers to promote, enrich and support
mathematics in schools and colleges. For more information visit our website:
Scan the QR
code to check the
solution and find
other problems.
www.furthermaths.org.uk
www.furthermaths.org.uk/favourite
NO
2
1
IN A SERIES OF SIX
This problem can be
solved in several ways,
using techniq ues from
GCSE or A level and
even beyond that!
The surprising result
fascinated Nobel
Prize winning Physicist
Richard Feynman.
A
A
5
B
B
C
C
A
4
A
3
B
B
C
C
ngle.
ia
r
t
y
n
a
h
it
w
t
1. Star
g each
n
lo
a
y
a
w
e
h
t
third of
e
n
o
t
in
o
p
a
orner.
k
c
h
c
a
e
2. Mar
m
o
r
f
lockwise
ic
t
n
a
g
in
v
o
edge m
ner to
r
o
c
’
e
it
s
o
p
p
s to the ‘o
t
in
o
p
e
s
e
h
t
3. Join
riangle.
t
w
e
n
a
e
k
a
m
the
is
le
g
n
ia
r
t
l
a
the origin
f
o
n
io
t
c
a
r
f
t
4. Wha
?
new triangle
tte
ematical Gaze
th
a
M
e
h
T
in
blem
Based on a pro
Further Mathematics Support Programme
The FMSP works with students and teachers to promote, enrich and support
mathematics in schools and colleges. For more information visit our website:
Scan the QR
code to check the
solution and find
other problems.
www.furthermaths.org.uk
www.furthermaths.org.uk/favourite
NO
6
IN A SERIES OF SIX
This deceptively
simple problem
can lead to
complicated algebra
but it does have a
concise and very
satisfying solution
A
hooks
d
n
o
p
a
f
o
e
g
m the ed
o
r
f
g
in
h
s
reels
fi
e
n
H
a
.
m
in
r
e
it
h
l
s
e
fi
e
r
A
egins to
b
d
n
a
A
n
io
it
he shore,
t
o
t
r
e
s
a fish at pos
lo
c
h
s
ging the fi
in
r
b
e
n
li
f
o
in 1m
ater.
w
e
h
t
f
o
e
c
a
f
sur
parallel to the
ore by:
h
s
e
h
t
o
t
r
e
s
clo
1m ?
ly
t
c
a
x
E
Is the fish now
r
o
;
s than 1m
s
e
L
;
m
1
n
a
h
More t
Further Mathematics Support Programme
The FMSP works with students and teachers to promote, enrich and support
mathematics in schools and colleges. For more information visit our website:
Scan the QR
code to check the
solution and find
other problems.
www.furthermaths.org.uk
www.furthermaths.org.uk/favourite