2016 AMC 12A Problem 6

Problem 6 of 25EasierNumber Theory Arithmetic

A triangular array of

2016

coins has

1

coin in the first row,

2

coins in the second row,

3

coins in the third row, and so on up to

N

coins in the

N

th row. What is the sum of the digits of

N?

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Solution

The total number of coins is

\begin{gathered} 1+2+\cdots+N\\ =\dfrac{N(N+1)}{2}\\ =2016, \end{gathered}

so

N(N+1)=4032.

Since

63\cdot 64=4032,

we have

N=63,

and the sum of its digits is

6+3=9.

Thus, the correct answer is D.

Tagged: triangular number · estimation

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