WMC 2018 Senior Problem 17

A triangle number n n is the sum of the first n n positive integers. For example, 10 10 is a triangle number because 1 + 2 + 3 + 4 = 10 1+2+3+4=10 . A repdigit number is one where all its digits are the same. For example, 55 55 is a repdigit number. There is just one 3 3 -digit triangular repdigit number. Find the sum of the digits that make up this number.

12 12 27 27 None of these 15 15 24 24

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1 solution

X X
Oct 14, 2018

A three-digit repdigit is a multiple of 111, so it is a multiple of 37 and 3.

36 × 37 2 = 666 \dfrac{36\times37}2=666 , so its digit sum is 18.

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