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AIME 2024 / AIME 2024 train 84d276b2-e6ba-5b59-8cc7-a3796bc9487c

Problem

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

Problem

There is a collection of

25

indistinguishable white chips and

25

indistinguishable black chips. Find the number of ways to place some of these chips in the

25

unit cells of a

5\times5

grid such that: each cell contains at most one chip all chips in the same row and all chips in the same column have the same colour any additional chip placed on the grid would violate one or more of the previous two conditions.

Plain-text mathematical notation (without MathML)

There is a collection of 25 indistinguishable white chips and 25 indistinguishable black chips. Find the number of ways to place some of these chips in the 25 unit cells of a 5×5 grid such that:

each cell contains at most one chip
all chips in the same row and all chips in the same column have the same colour
any additional chip placed on the grid would violate one or more of the previous two conditions.

Original LaTeX notation

There is a collection of $25$ indistinguishable white chips and $25$ indistinguishable black chips. Find the number of ways to place some of these chips in the $25$ unit cells of a $5\times5$ grid such that:

each cell contains at most one chip
all chips in the same row and all chips in the same column have the same colour
any additional chip placed on the grid would violate one or more of the previous two conditions.

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Source and history

task_id: 84d276b2-e6ba-5b59-8cc7-a3796bc9487c
task_key: default--train--84d276b2-e6ba-5b59-8cc7-a3796bc9487c
task_revision_id: 2
config / split: default / train

Official source

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