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2011 Greece Junior Math Olympiad
2
2
Part of
2011 Greece Junior Math Olympiad
Problems
(1)
Number Theory
Source: Archimedes Junior 2011
3/16/2020
We consider the set of four-digit positive integers
x
=
a
b
c
d
‾
x =\overline{abcd}
x
=
ab
c
d
with digits different than zero and pairwise different. We also consider the integers
y
=
d
c
b
a
‾
y = \overline{dcba}
y
=
d
c
ba
and we suppose that
x
>
y
x > y
x
>
y
. Find the greatest and the lowest value of the difference
x
−
y
x-y
x
−
y
, as well as the corresponding four-digit integers
x
,
y
x,y
x
,
y
for which these values are obtained.
number theory