MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
2013 Greece Junior Math Olympiad
3
3
Part of
2013 Greece Junior Math Olympiad
Problems
(1)
Four digit numbers
Source: Archimedes Junior 2013
3/16/2020
Let
A
=
a
b
c
d
‾
A=\overline{abcd}
A
=
ab
c
d
be a four-digit positive integer with digits
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
, such that
a
≥
7
a\ge7
a
≥
7
and
a
>
b
>
c
>
d
>
0
a>b>c>d>0
a
>
b
>
c
>
d
>
0
. Consider the positive integer
B
=
d
c
b
a
‾
B=\overline{dcba}
B
=
d
c
ba
, that comes from number
A
A
A
by reverting the order of it's digits. Given that the number
A
+
B
A+B
A
+
B
has all it's digits odd, find all possible values of number
A
A
A
.
combinatorics