2018 AMC 10A Problems/Problem 17
Problem
Let be a set of 6 integers taken from
with the property that if
and
are elements of
with
, then
is not a multiple of
. What is the least possible values of an element in
Solution
Intuitively, one would see this list and start with prime numbers. However, there are only 5 prime numbers less than , making this impossible. It is also clear that another number can't be added in, so
can't be the smallest. Next, we start the sequence with
, and a bit of trial and error shows it's impossible. Lastly, starting with
, we find that the sequence
works, giving us
.
(Random_Guy)
See Also
2018 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 AMC 10 Problems and Solutions |
2018 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
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 AMC 12 Problems and Solutions |
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