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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_8 / How many nonempty subsets B of 0,1,2,3,⋯,12 have the property that the number of elements in B is equal to the least element of B? For example, B=4,6,8,11 satisfies the condition.

Problem

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

problem

How many nonempty subsets

B

{0, 1, 2, 3, \cdots, 12}

have the property that the number of elements in

B

is equal to the least element of

B

? For example,

B = {4, 6, 8, 11}

satisfies the condition.

Plain-text mathematical notation (without MathML)

How many nonempty subsets B of 0,1,2,3,⋯,12 have the property that the number of elements in B is equal to the least element of B? For example, B=4,6,8,11 satisfies the condition.

Original LaTeX notation

How many nonempty subsets $B$ of ${0, 1, 2, 3, \cdots, 12}$ have the property that the number of elements in $B$ is equal to the least element of $B$? For example, $B = {4, 6, 8, 11}$ satisfies the condition.

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_8
task_id: 3130ab13-88fb-5806-b4d8-72854ccc97c9
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f8
task_revision_id: 2
config / split: default / train

Official source

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