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

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question

There are 8!=403208!=40320 eight-digit positive integers that use each of the digits 1,2,3,4,5,6,7,81,2,3,4,5,6,7,8 exactly once. Let NN be the number of these integers that are divisible by 22. Find the difference between NN 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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Source and history

task_id
a610c01b-01ff-53ef-93a4-48ad1f50536b
task_key
AIME2025~2dI--test--a610c01b-01ff-53ef-93a4-48ad1f50536b
task_revision_id
3
config / split
AIME2025-I / test

Official source

initial import