2016 AMC 10A Problems/Problem 14
Problem
How many ways are there to write as the sum of twos and threes, ignoring order? (For example,
and
are two such ways.)
Solution 1
The amount of twos in our sum ranges from to
, with differences of
because
.
The possible amount of twos is
Solution 2
You can also see that you can rewrite the word problem into a equation +
=
. Therefore the question is just how many multiples of 3 subtracted from 16 will be an even number. We can see if
= 0,
= 1008. All the way to
= 0, and
=
.Therefore, between
and
, the number of multiples of 2 is (C) 337.