# 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