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AIME 2024 / AIME 2024 train 25b99ad9-53e1-50fb-b064-a87f7fee5801

Problem

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

Problem

Consider the paths of length

16

that follow the lines from the lower left corner to the upper right corner on an

8\times 8

grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.

Plain-text mathematical notation (without MathML)

Consider the paths of length 16 that follow the lines from the lower left corner to the upper right corner on an 8×8 grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.

Original LaTeX notation

Consider the paths of length $16$ that follow the lines from the lower left corner to the upper right corner on an $8\times 8$ grid. Find the number of such paths that change direction exactly four times, as in the examples shown below.

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Source and history

task_id: 25b99ad9-53e1-50fb-b064-a87f7fee5801
task_key: default--train--25b99ad9-53e1-50fb-b064-a87f7fee5801
task_revision_id: 2
config / split: default / train

Official source

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