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Cono Sur Olympiad
1997 Cono Sur Olympiad
5
5
Part of
1997 Cono Sur Olympiad
Problems
(1)
Number Theory + Combinat
Source: Cono sur Olympiad 1997 P5
10/11/2017
Let
n
n
n
be a natural number
n
>
3
n>3
n
>
3
. Show that in the multiples of
9
9
9
less than
1
0
n
10^n
1
0
n
, exist more numbers with the sum of your digits equal to
9
(
n
−
2
)
9(n - 2)
9
(
n
−
2
)
than numbers with the sum of your digits equal to
9
(
n
−
1
)
9(n - 1)
9
(
n
−
1
)
.
combinatorics
number theory
cono sur