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OlympiadBench / 2152 / In a 999×999 square table some cells are white and the remaining ones…

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

In a

999 \times 999

square table some cells are white and the remaining ones are red. Let

T

be the number of triples

\left(C_{1}, C_{2}, C_{3}\right)

of cells, the first two in the same row and the last two in the same column, with

C_{1}

and

C_{3}

white and

C_{2}

red. Find the maximum value

T

can attain.

Plain-text mathematical notation (without MathML)

In a 999×999 square table some cells are white and the remaining ones are red. Let T be the number of triples (C₁,C₂,C₃) of cells, the first two in the same row and the last two in the same column, with C₁ and C₃ white and C₂ red. Find the maximum value T can attain.

Original LaTeX notation

In a $999 \times 999$ square table some cells are white and the remaining ones are red. Let $T$ be the number of triples $\left(C_{1}, C_{2}, C_{3}\right)$ of cells, the first two in the same row and the last two in the same column, with $C_{1}$ and $C_{3}$ white and $C_{2}$ red. Find the maximum value $T$ can attain.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2152
task_id: 0a3f91c7-b79f-576f-af3c-e3471c2c2660
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2152
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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