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Omni-MATH / From a set of integers {1,...,100}, k integers were deleted. Is it always possible to choose k distinct integers from the remaining set such that their sum is 100 if [b](a) k=9?[/b…

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problem

From a set of integers {1,...,100}\{1,...,100\}, kk integers were deleted. Is it always possible to choose kk distinct integers from the remaining set such that their sum is 100100 if [b](a) k=9k=9?[/b] [b](b) k=8k=8?[/b]
Plain-text mathematical notation (without MathML)
From a set of integers {1,...,100}, k integers were deleted. Is it always possible to choose k distinct integers from the remaining set such that their sum is 100 if

[b](a) k=9?[/b]
[b](b) k=8?[/b]
Original LaTeX notation
From a set of integers $\{1,...,100\}$, $k$ integers were deleted. Is it always possible to choose $k$ distinct integers from the remaining set such that their sum is $100$ if

[b](a) $k=9$?[/b]
[b](b) $k=8$?[/b]

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Source and history

task_id
d26fdf84-4974-57dc-ac5b-8064538fd9e9
task_key
test--d26fdf84-4974-57dc-ac5b-8064538fd9e9
task_revision_id
1
config / split
/ test

Official source

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