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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.

question

In a 999×999999 \times 999 square table some cells are white and the remaining ones are red. Let TT be the number of triples (C1,C2,C3)\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 C1C_{1} and C3C_{3} white and C2C_{2} red. Find the maximum value TT 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.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

Discussion

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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
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import