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National and Regional Contests
Turkey Contests
Turkey Team Selection Test
2016 Turkey Team Selection Test
7
7
Part of
2016 Turkey Team Selection Test
Problems
(1)
Arithmetic Sequence in Every Intersection
Source: Turkey TST 2016 P7
4/10/2016
A
1
,
A
2
,
…
A
k
A_1, A_2,\dots A_k
A
1
,
A
2
,
…
A
k
are different subsets of the set
{
1
,
2
,
…
,
2016
}
\{1,2,\dots ,2016\}
{
1
,
2
,
…
,
2016
}
. If
A
i
∩
A
j
A_i\cap A_j
A
i
∩
A
j
forms an arithmetic sequence for all
1
≤
i
<
j
≤
k
1\le i <j\le k
1
≤
i
<
j
≤
k
, what is the maximum value of
k
k
k
?
arithmetic sequence
combinatorics