jmc

The five numbers which cause people to leave the circle are $7,14,17,21,$ and $27.$ The most straightforward way to do this would be to draw out the circle with the people, and cross off people as you count. Assuming the six people start with $1$, Arn counts $7$ so he leaves first. Then, Cyd counts $14$ as there are $7$ numbers to be counted from this point. Then, Fon, Bob, and Eve, count, $17,$ $21,$ and $27$, respectively, so the last one standing is Dan. Hence, the answer would be $\boxed{\text{Dan}}$.