Question

There are blue, red and green pencils in the box—20 pencils total. There are 6 times more green pencils than blue pencils. There are fewer red pencils than green pencils. How many pencils do you need to take out of the box in order to get at least one red pencil among them?

Answer 1

You have to take 15 pens to get at least one red pencil.

Explanation:

If there were one red and 6 green pens, there would be more red than green pens.

If there were 3 or more blue and thus 18 or more green pens, the number of pens would be over 20.

So there must be 2 blue, 12 green and thus 6 red pencils. So you have to take at least 15 pens to be sure that you got a red one.