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Omni-MATH / Let n be an positive integer. Find the smallest integer k with the following property; Given any real numbers a₁,⋯,a_(d) such that a₁+a₂+⋯+a_(d)=n and 0≤a_(i)≤1 for i=1,2,⋯,d, it i…

Problem

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problem

Let nn be an positive integer. Find the smallest integer kk with the following property; Given any real numbers a1,⋯,ada_1 , \cdots , a_d such that a1+a2+⋯+ad=na_1 + a_2 + \cdots + a_d = n and 0≤ai≤10 \le a_i \le 1 for i=1,2,⋯,di=1,2,\cdots ,d, it is possible to partition these numbers into kk groups (some of which may be empty) such that the sum of the numbers in each group is at most 11.
Plain-text mathematical notation (without MathML)
Let n be an positive integer. Find the smallest integer k with the following property; Given any real numbers a₁,⋯,a_(d) such that a₁+a₂+⋯+a_(d)=n and 0≤a_(i)≤1 for i=1,2,⋯,d, it is possible to partition these numbers into k groups (some of which may be empty) such that the sum of the numbers in each group is at most 1.
Original LaTeX notation
Let $n$ be an positive integer. Find the smallest integer $k$ with the following property; Given any real numbers $a_1 , \cdots , a_d $ such that $a_1 + a_2 + \cdots + a_d = n$ and $0 \le a_i \le 1$ for $i=1,2,\cdots ,d$, it is possible to partition these numbers into $k$ groups (some of which may be empty) such that the sum of the numbers in each group is at most $1$.

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Source and history

task_id
5de12c04-b1bf-5d46-a773-0d8e9e5f370f
task_key
test--5de12c04-b1bf-5d46-a773-0d8e9e5f370f
task_revision_id
1
config / split
/ test

Official source

initial import