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AIME 2025 I / There are 8!=40320 eight-digit positive integers that use each of the digits…

Problem

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question

There are

8!=40320

eight-digit positive integers that use each of the digits

1,2,3,4,5,6,7,8

exactly once. Let

N

be the number of these integers that are divisible by 22. Find the difference between

N

and 2025.

Plain-text mathematical notation (without MathML)

There are 8!=40320 eight-digit positive integers that use each of the digits 1,2,3,4,5,6,7,8 exactly once. Let N be the number of these integers that are divisible by 22. Find the difference between N and 2025.

Original LaTeX notation

There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.

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task_id: a610c01b-01ff-53ef-93a4-48ad1f50536b
task_key: AIME2025~2dI--test--a610c01b-01ff-53ef-93a4-48ad1f50536b
task_revision_id: 2
config / split: AIME2025-I / test

Official source

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