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)