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International Zhautykov Olympiad
2023 International Zhautykov Olympiad
4
4
Part of
2023 International Zhautykov Olympiad
Problems
(1)
Possible sums of sequence with zero-sum
Source: IZHO 2023 P4
2/6/2023
The sum of
n
>
2
n > 2
n
>
2
nonzero real numbers (not necessarily distinct) equals zero. For each of the
2
n
ā
1
2^n - 1
2
n
ā
1
ways to choose one or more of these numbers, their sums are written in non-increasing order in a row. The first number in the row is
S
S
S
. Find the smallest possible value of the second number.
algebra