2016 AMC 10A Problems/Problem 14
Contents
[hide]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
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
subtracted from 2016 will be an even number. We can see that
,
all the way to
, and
works, with
being incremented by
's.Therefore, between
and
, the number of multiples of
is
.
See Also
2016 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AMC 10 Problems and Solutions |
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