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OlympiadBench / 1775 / Given a positive integer n, find the smallest value of…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Given a positive integer

n

, find the smallest value of

\left\lfloor\frac{a_{1}}{1}\right\rfloor+\left\lfloor\frac{a_{2}}{2}\right\rfloor+\cdots+\left\lfloor\frac{a_{n}}{n}\right\rfloor

over all permutations

\left(a_{1}, a_{2}, \ldots, a_{n}\right)

(1,2, \ldots, n)

Plain-text mathematical notation (without MathML)

Given a positive integer n, find the smallest value of ⌊(a₁)/(1)⌋+⌊(a₂)/(2)⌋+⋯+⌊(a_(n))/(n)⌋ over all permutations (a₁,a₂,…,a_(n)) of (1,2,…,n).

Original LaTeX notation

Given a positive integer $n$, find the smallest value of $\left\lfloor\frac{a_{1}}{1}\right\rfloor+\left\lfloor\frac{a_{2}}{2}\right\rfloor+\cdots+\left\lfloor\frac{a_{n}}{n}\right\rfloor$ over all permutations $\left(a_{1}, a_{2}, \ldots, a_{n}\right)$ of $(1,2, \ldots, n)$.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1775
task_id: a2455d95-c0b4-59ed-9ab3-a61b16f8218c
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1775
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import