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Lusophon Mathematical Olympiad
2021 Lusophon Mathematical Olympiad
1
1
Part of
2021 Lusophon Mathematical Olympiad
Problems
(1)
Sextalternado numbers
Source: Lusophon Matematical Olympiad 2021 Problem 1
12/19/2021
Juca has decided to call all positive integers with 8 digits as
s
e
x
t
a
l
t
e
r
n
a
d
o
s
sextalternados
se
x
t
a
lt
er
na
d
os
if it is a multiple of 30 and its consecutive digits have different parity. At the same time, Carlos decided to classify all
s
e
x
t
a
l
t
e
r
n
a
d
o
s
sextalternados
se
x
t
a
lt
er
na
d
os
that are multiples of 12 as
s
u
p
e
r
s
e
x
t
a
l
t
e
r
n
a
d
o
s
super sextalternados
s
u
p
erse
x
t
a
lt
er
na
d
os
.a) Show that
s
u
p
e
r
s
e
x
t
a
l
t
e
r
n
a
d
o
s
super sextalternados
s
u
p
erse
x
t
a
lt
er
na
d
os
numbers don't exist.b) Find the smallest
s
e
x
t
a
l
t
e
r
n
a
d
o
sextalternado
se
x
t
a
lt
er
na
d
o
number.
number theory