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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2019 Moldova Team Selection Test
3
3
Part of
2019 Moldova Team Selection Test
Problems
(1)
Ez pz combinatorics
Source: Moldova TST 2019
3/8/2019
On the table there are written numbers
673
,
674
,
⋯
,
2018
,
2019.
673, 674, \cdots, 2018, 2019.
673
,
674
,
⋯
,
2018
,
2019.
Nibab chooses arbitrarily three numbers
a
,
b
a,b
a
,
b
and
c
c
c
, erases them and writes the number
min
(
a
,
b
,
c
)
3
\frac{\min(a,b,c)}{3}
3
m
i
n
(
a
,
b
,
c
)
, then he continues in an analogous way. After Nibab performed this operation
673
673
673
times, on the table remained a single number
k
k
k
. Prove that
k
∈
(
0
,
1
)
.
k\in(0,1).
k
∈
(
0
,
1
)
.
combinatorics
TST
easy