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UKMT Pink Kangaroo, 2018

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each positive integer $n$ occurs $n$ times.) How many of the first 105 numbers in this sequence are divisible by 3?

(A) $4$ (B) $12$ (C) $21$ (D) $30$ (E) $45$

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