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4
3
2
1
Grade 7
/ Preparing for the Olympics
5 exercises (100% corrected)
a
Logic
(2 exercices)
Euclidean division
(1 exercice)
Arithmetic
(1 exercice)
With a little algebra
(1 exercice)
377
3
×
7
×
7
147
1
×
4
×
7
28
2
×
8
16
1
×
6
6
1
2
3
4
5
6
7
8
9
10
11
12
a
1
a
2
a
3
a
4
a
5
a
6
a
7
a
8
a
9
a
10
a
11
a
12
C
1.
L
o
gic
E.10821
P
eter
is
a
n
um
b
ers
en
th
usiast.
He
has
a
four-digit
digital
clo
c
k
in
his
car
that
tells
the
time
from
00:
00
to
23:
59
.
As
he
lea
v
es
for
a
long
trip,
P
eter
observ
es
his
clo
c
k
and
no-
tices
that
the
t
w
o
n
um
b
ers
sho
wn,
the
min
utes
and
the
hours,
are
squares
of
whole
n
um
b
ers
(which,
on
a
digital
clo
ck,
ar
e
written
as
:00,
01,
04,
09,
25,.
.
.
)
After
returning
from
his
trip,
P
eter
finds
that
his
clo
c
k
is
once
again
displa
ying
squares
of
t
w
o
whole
n
um
b
ers.
His
on
b
oard
computer
tells
him
that
he
has
tra
v
eled
352
k
m
in
4
hours
and
20
min
utes.
When
can
P
eter
b
e
home
from
his
trip?
E.10823
The
p
ersistence
of
a
n
um
b
er
In
this
exercise,
w
e
consider
in
tegers
greater
than
or
equal
to
10
,
written
in
the
decimal
system.
When
w
e
m
ultiply
the
digits
that
mak
e
up
the
writing
of
an
in
teger,
w
e
get
a
new
n
um
b
er.
W
e
rep
eat
this
calculation
with
this
new
n
um
b
er
and
so
on.
F
or
example,
for
the
n
um
b
er
377
:
The
pro
cess
stops
when
w
e
get
a
n
um
b
er
written
with
only
one
digit.
It
to
ok
4
steps
in
all
:
w
e
sa
y
that
the
p
ersistence
of
377
is
4
.
1
What
is
the
p
ersistence
of
eac
h
of
the
n
um
b
ers
a
77
b
28
534
c
6
785
791
2
The
p
ersistence
of
eac
h
of
the
n
um
b
ers
2
019
,
4
806
,
and
13
970
875
is
equal
to
1
.
What
general
result
do
these
results
seem
to
illustrate?
Justify
.
3
Is
there
a
digit
that
could
b
e
inserted
in
to
the
writing
of
a
n
um
b
er
without
c
hanging
its
p
ersistence?
4
Find
a
n
um
b
er
written
with
20
digits
whose
p
ersistence
is
4
.
5
What
are
the
p
ossible
p
ersistences
of
a
n
um
b
er
whose
writing
includes
an
ev
en
n
um
b
er
and
5?
2.
Euclide
an
division
E.10822
The
frieze
A
frieze
is
made
b
y
cop
ying
to
the
righ
t
the
pattern
made
up
of
the
t
w
elv
e
columns
sho
wn
b
elo
w
:
Eac
h
column
of
the
frieze
is
co
ded
with
three
sym
b
ols,
000
if
all
three
b
o
xes
(of
the
c
olumn)
are
white,
001
if
the
top
t
w
o
squares
are
white
and
the
third
noire.
.
.
and
finally
111
if
all
three
squares
are
blac
k.
1
Ho
w
is
the
10
column
of
the
frieze
co
ded?
Same
question
for
the
14
column.
2
In
the
ab
o
v
e
pattern,
giv
e
the
colonne
(s)
co
ded
100
?
3
W
e
are
giv
en
an
in
teger
n
.
Ho
w
is
the
column
12
n
+5
co
ded?
4
Ho
w
is
the
column
2
017
co
ded?
3.
A
rithmetic
E.10824
The
EAN-13
(EEur
op
e
an
A
rti-
cle
Numb
ering)
is
a
barco
de
used
b
y
trade
and
industry
to
uniquely
iden
tify
ob
jects
and
b
e
read
b
y
a
scanner.
This
bar-
co
de
consists
of
13
digits
(inte
gers
b
etwe
en
0
and
9
)
,
the
last
one
b
eing
a
con
trol
k
ey
calculated
from
the
previous
12
digits.
A
barco
de
is
sym
b
olized
b
y
the
follo
wing
table
:
.
.
.
where
the
thirteen
digits
making
up
the
barco
de
ha
v
e
b
een
carried.
The
n
um
b
er
C
is
the
v
erification
k
ey
.
T
o
determine
this,
w
e
calculate
:
S
=
a
1
+
a
3
+
a
5
+
a
7
+
a
9
+
a
11
+3
×
a
2
+
a
4
+
a
6
+
a
8
+
a
10
+
a
12
.
C
is
then
the
n
um
b
er
suc
h
that
S
+
C
is
a
m
ultiple
of
10
.
1
is
co
de
4971850187820
v
alid?
2
Determine
C
for
the
co
de
978204732850
C
to
b
e
v
alid.
3
A
digit
has
b
een
replaced
with
x
in
the
co
de
32525
x
7041767
.
What
v
alue
should
b
e
giv
en
to
x
for
this
co
de
to
b
e
v
alid?
4
The
co
de
3742278085985
is
not
v
alid.
What
can
b
e
the
v
alues
of
the
first
t
w
o
digits
on
the
left
in
other
v
alid
co
des
with
the
11
same
digits
on
the
righ
t?
4.
With
a
little
algebr
a
h
ttps:/
/c
hingmath.fr
chapExoCorrec/10821
sacados/10821
chapExoCorrec/10823
sacados/10823
377
3
×
7
×
7
147
1
×
4
×
7
28
2
×
8
16
1
×
6
6
chapExoCorrec/10822
sacados/10822
1
2
3
4
5
6
7
8
9
10
11
12
chapExoCorrec/10824
sacados/10824
a
1
a
2
a
3
a
4
a
5
a
6
a
7
a
8
a
9
a
10
a
11
a
12
C
E.10825
A
calculation
program
Here
is
a
calculation
program
:
Let
N
b
e
a
natural
n
um
b
er
written
in
the
decimal
system
:
Step
n
o
1
:
Iden
tify
the
digit
X
of
the
units
of
N
.
Step
n
o
2
:
Calculate
N
−
X
.
Let
M
b
e
the
n
um
b
er
ob-
tained.
Step
n
o
3
:
Divide
M
b
y
10
.
Let
D
b
e
the
n
um
b
er
ob-
tained.
Step
n
o
4
:
Calculate
D
+
2
X
.
Let
R
b
e
the
n
um
b
er
ob-
tained.
Step
n
o
5
:
If
R
is
differen
t
from
N
,
then
go
to
step
n
o
6.
Otherwise,
stop
and
displa
y
R
.
Step
n
o
6
:
If
R
is
written
with
a
single
digit,
then
stop
and
displa
y
R
.
Otherwise,
giv
e
N
the
v
alue
R
and
resume
the
calculation
program
at
step
n
o
1.
1
What
result
is
displa
y
ed
when
N
=
15
is
en
tered
in
to
the
calculation
program?
2
What
happ
ens
when
N
=
2015
is
en
tered
in
to
the
calcu-
lation
program?
h
ttps:/
/c
hingmath.fr
chapExoCorrec/10825
sacados/10825
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