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OlympiadBench / 1694 / Determine the greatest positive integer k that satisfies the following…

Problem

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

answer type

Numerical

is multiple answer

false

language

English

question

Determine the greatest positive integer

k

that satisfies the following property: The set of positive integers can be partitioned into

k

subsets

A_{1}, A_{2}, \ldots, A_{k}

such that for all integers

n \geq 15

and all

i \in\{1,2, \ldots, k\}

there exist two distinct elements of

A_{i}

whose sum is

n

Plain-text mathematical notation (without MathML)

Determine the greatest positive integer k that satisfies the following property: The set of positive integers can be partitioned into k subsets A₁,A₂,…,A_(k) such that for all integers n≥15 and all i∈{1,2,…,k} there exist two distinct elements of A_(i) whose sum is n.

Original LaTeX notation

Determine the greatest positive integer $k$ that satisfies the following property: The set of positive integers can be partitioned into $k$ subsets $A_{1}, A_{2}, \ldots, A_{k}$ such that for all integers $n \geq 15$ and all $i \in\{1,2, \ldots, k\}$ there exist two distinct elements of $A_{i}$ whose sum is $n$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1694
task_id: 055e365c-6619-5097-b445-57e73dfc6cc3
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1694
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import