[Text problems] [Case enumeration]

In a box, there are blue, red, and green pencils. In total, there are 20 pieces. The number of blue pencils is 6 times the number of green pencils, and the number of red pencils is less than the number of blue pencils. How many red pencils are in the box?
Think about how many blue pencils there can be.

## Solution

Since there are 20 pencils in total, and blue and green pencils together make up 7 parts. This means there can be 6 or 12 blue pencils, and green and red pencils would then be 1 and 13 or 2 and 6, respectively. Since there are fewer red pencils than blue ones, only the second option is possible: 12 blue, 2 green, and 6 red.