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OlympiadBench / 2185 / Let m be a positive integer. Consider a 4m×4m array of square unit…

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

m

be a positive integer. Consider a

4 m \times 4 m

array of square unit cells. Two different cells are related to each other if they are in either the same row or in the same column. No cell is related to itself. Some cells are coloured blue, such that every cell is related to at least two blue cells. Determine the minimum number of blue cells.

Plain-text mathematical notation (without MathML)

Let m be a positive integer. Consider a 4m×4m array of square unit cells. Two different cells are related to each other if they are in either the same row or in the same column. No cell is related to itself. Some cells are coloured blue, such that every cell is related to at least two blue cells. Determine the minimum number of blue cells.

Original LaTeX notation

Let $m$ be a positive integer. Consider a $4 m \times 4 m$ array of square unit cells. Two different cells are related to each other if they are in either the same row or in the same column. No cell is related to itself. Some cells are coloured blue, such that every cell is related to at least two blue cells. Determine the minimum number of blue cells.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2185
task_id: 0b492756-499d-55a2-b31b-7a3855819018
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2185
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import