Difference between revisions of "2016 AMC 10A Problems/Problem 14"
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| + | ==Problem== | ||
| + | How many ways are there to write <math>2016</math> as the sum of twos and threes, ignoring order? (For example, <math>1008\cdot 2 + 0\cdot 3</math> and <math>402\cdot 2 + 404\cdot 3</math> are two such ways.) | ||
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| + | <math>\textbf{(A)}\ 236\qquad\textbf{(B)}\ 336\qquad\textbf{(C)}\ 337\qquad\textbf{(D)}\ 403\qquad\textbf{(E)}\ 672</math> | ||
==Solution== | ==Solution== | ||
Revision as of 18:59, 3 February 2016
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
The amount of twos in our sum ranges from 
to 
, with differences of 
because 
.
The possible amount of twos is 
