# Difference between revisions of "2018 AMC 8 Problems/Problem 3"

## Problem 3

Students Arn, Bob, Cyd, Dan, Eve, and Fon are arranged in that order in a circle. They start counting: Arn first, then Bob, and so forth. When the number contains a 7 as a digit (such as 47) or is a multiple of 7 that person leaves the circle and the counting continues. Who is the last one present in the circle? $\textbf{(A) } \text{Arn}\qquad\textbf{(B) }\text{Bob}\qquad\textbf{(C) }\text{Cyd}\qquad\textbf{(D) }\text{Dan}\qquad \textbf{(E) }\text{Eve}$

## Solution

The five numbers which cause people to leave the circle are $7, 14, 17, 21,$ and $27.$

Arn counts $7$ (assuming they start at $1$) so he leaves first. Then Cyd counts $14$, as there are $7$ numbers to be counted from this point. Then Fon, Bob, Eve, so last one standing is Dan, hence meaning the answer would be $\textbf{(D)}$

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