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2022 AMC 12A Problems/Problem 16

Revision as of 20:59, 11 November 2022 by Stevenyiweichen (talk | contribs) (Created page with "==Problem== A \emph{triangular number} is a positive integer that can be expressed in the form <math>t_n = 1+2+3+\cdots+n</math>, for some positive integer <math>n</math>. Th...")
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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?

Solution

https://youtu.be/08YkinzFcCc

(Professor Chen Education Palace, www.professorchenedu.com)

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