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Problems
Contests
National and Regional Contests
Peru Contests
Peru Cono Sur TST
2006 Team Selection Test For CSMO
3
3
Part of
2006 Team Selection Test For CSMO
Problems
(1)
Xvii cono sur - peru tst 2006.
Source: Spanish Communities
4/4/2006
The set
M
=
{
1
;
2
;
3
;
…
;
29
;
30
}
M= \{1;2;3;\ldots ; 29;30\}
M
=
{
1
;
2
;
3
;
…
;
29
;
30
}
is divided in
k
k
k
subsets such that if
a
+
b
=
n
2
,
(
a
,
b
∈
M
,
a
≠
b
,
n
a+b=n^2, (a,b \in M, a\neq b, n
a
+
b
=
n
2
,
(
a
,
b
∈
M
,
a
=
b
,
n
is an integer number
)
)
)
, then
a
a
a
and
b
b
b
belong different subsets. Determine the minimum value of
k
k
k
.
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combinatorics unsolved
combinatorics