2018 AMC 8 Problems/Problem 3
Contents
Problem
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?
Solution 1
The five numbers which cause people to leave the circle are and
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 , Arn counts
so he leaves first. Then, Cyd counts
as there are
numbers to be counted from this point. Then, Fon, Bob, and Eve, count,
and
, respectively, so the last one standing is Dan. Hence, the answer would be
.
Video Solution
~savannahsolver
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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