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OlympiadBench / 1662 / Let n>1 be an integer. In the space, consider the set

Problem

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

answer type

Expression

is multiple answer

false

language

English

question

Let

n>1

be an integer. In the space, consider the set

S=\{(x, y, z) \mid x, y, z \in\{0,1, \ldots, n\}, x+y+z>0\}

Find the smallest number of planes that jointly contain all

(n+1)^{3}-1

points of

S

but none of them passes through the origin.

Plain-text mathematical notation (without MathML)

Let n>1 be an integer. In the space, consider the set
S={(x,y,z)∣x,y,z∈{0,1,…,n},x+y+z>0}
Find the smallest number of planes that jointly contain all (n+1)³−1 points of S but none of them passes through the origin.

Original LaTeX notation

Let $n>1$ be an integer. In the space, consider the set
$$
S=\{(x, y, z) \mid x, y, z \in\{0,1, \ldots, n\}, x+y+z>0\}
$$
Find the smallest number of planes that jointly contain all $(n+1)^{3}-1$ points of $S$ but none of them passes through the origin.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1662
task_id: 6e87939f-a840-5d1f-a9f4-d46e70496db6
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1662
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import