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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_16 / A emph{triangular number} is a positive integer that can be expressed in the form t_(n)=1+2+3+⋯+n, for some positive integer n. The three smallest triangular numbers that are also …

Problem

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problem

A $\emph{triangular number}$ is a positive integer that can be expressed in the form

t_n = 1+2+3+\cdots+n

, for some positive integer

n

. The three smallest triangular numbers that are also perfect squares are

t_1 = 1 = 1^2

t_8 = 36 = 6^2

, and

t_{49} = 1225 = 35^2

. What is the sum of the digits of the fourth smallest triangular number that is also a perfect square?

Plain-text mathematical notation (without MathML)

A $\emph{triangular number}$ is a positive integer that can be expressed in the form t_(n)=1+2+3+⋯+n, for some positive integer n. The three smallest triangular numbers that are also perfect squares are
t₁=1=1², t₈=36=6², and t₄₉=1225=35². What is the sum of the digits of the fourth smallest triangular number that is also a perfect square?

Original LaTeX notation

A $\emph{triangular number}$ is a positive integer that can be expressed in the form $t_n = 1+2+3+\cdots+n$, for some positive integer $n$. The three smallest triangular numbers that are also perfect squares are
$t_1 = 1 = 1^2$, $t_8 = 36 = 6^2$, and $t_{49} = 1225 = 35^2$. What is the sum of the digits of the fourth smallest triangular number that is also a perfect square?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_16
task_id: e6693d76-6762-557d-be27-abbd9382e8a0
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f16
task_revision_id: 2
config / split: default / train

Official source

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