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AIME 2024 / AIME 2024 train cec2826e-297a-503f-89b5-ed57c3bc02a7

Problem

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

Problem

Alice chooses a set

A

of positive integers. Then Bob lists all finite nonempty sets

B

of positive integers with the property that the maximum element of

B

belongs to

A

. Bob's list has 2024 sets. Find the sum of the elements of A.

Plain-text mathematical notation (without MathML)

Alice chooses a set A of positive integers. Then Bob lists all finite nonempty sets B of positive integers with the property that the maximum element of B belongs to A. Bob's list has 2024 sets. Find the sum of the elements of A.

Original LaTeX notation

Alice chooses a set $A$ of positive integers. Then Bob lists all finite nonempty sets $B$ of positive integers with the property that the maximum element of $B$ belongs to $A$. Bob's list has 2024 sets. Find the sum of the elements of A.

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Source and history

task_id: cec2826e-297a-503f-89b5-ed57c3bc02a7
task_key: default--train--cec2826e-297a-503f-89b5-ed57c3bc02a7
task_revision_id: 2
config / split: default / train

Official source

initial import