MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
2000 Canada National Olympiad
3
3
Part of
2000 Canada National Olympiad
Problems
(1)
Sum
Source: Canada 2000
3/4/2006
Let
A
=
(
a
1
,
a
2
,
⋯
,
a
2000
)
A = (a_1, a_2, \cdots ,a_{2000})
A
=
(
a
1
,
a
2
,
⋯
,
a
2000
)
be a sequence of integers each lying in the interval
[
−
1000
,
1000
]
[-1000,1000]
[
−
1000
,
1000
]
. Suppose that the entries in A sum to
1
1
1
. Show that some nonempty subsequence of
A
A
A
sums to zero.
combinatorics unsolved
combinatorics