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National and Regional Contests
Turkey Contests
Turkey MO (2nd round)
2004 Turkey MO (2nd round)
6
Turkey NMO 2004, Find the number of elements of K(2004,2004)
Turkey NMO 2004, Find the number of elements of K(2004,2004)
Source:
December 11, 2010
combinatorics unsolved
combinatorics
Problem Statement
Define
K
(
n
,
0
)
=
∅
K(n,0)=\varnothing
K
(
n
,
0
)
=
∅
and, for all nonnegative integers m and n,
K
(
n
,
m
+
1
)
=
{
k
∣
1
≤
k
≤
n
and
K
(
k
,
m
)
∩
K
(
n
−
k
,
m
)
=
∅
}
K(n,m+1)=\left\{ \left. k \right|\text{ }1\le k\le n\text{ and }K(k,m)\cap K(n-k,m)=\varnothing \right\}
K
(
n
,
m
+
1
)
=
{
k
∣
1
≤
k
≤
n
and
K
(
k
,
m
)
∩
K
(
n
−
k
,
m
)
=
∅
}
. Find the number of elements of
K
(
2004
,
2004
)
K(2004,2004)
K
(
2004
,
2004
)
.
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