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Contests
National and Regional Contests
Ecuador Contests
Ecuador Juniors
2019 Ecuador Juniors
1
1
Part of
2019 Ecuador Juniors
Problems
(1)
Ecuadorian 3-digit numbers - 2019 Ecuador Juniors (OMEC) L2 p1
Source:
10/24/2022
A three-digit
a
b
c
‾
\overline{abc}
ab
c
number is called Ecuadorian if it meets the following conditions:
∙
\bullet
∙
a
b
c
‾
\overline{abc}
ab
c
does not end in
0
0
0
.
∙
\bullet
∙
a
b
c
‾
\overline{abc}
ab
c
is a multiple of
36
36
36
.
∙
\bullet
∙
a
b
c
‾
−
c
b
a
‾
\overline{abc} - \overline{cba}
ab
c
−
c
ba
is positive and a multiple of
36
36
36
. Determine all the Ecuadorian numbers.
number theory
Digits