There are a few red and a few green balls in a box, Blind folded, you have to take out 7 balls to have a red for sure,and you have to take out 13 to have a ball from both colours for sure. How many green and how many red balls are there in the box?

To solve this problem, let's break it down step by step.

First, let's assume there are "r" red balls and "g" green balls in the box.

To guarantee getting a red ball, we need to take out 7 balls. So, from those 7 balls, we want at least 1 red ball. This means the worst-case scenario is that we pick all the green balls in those 7 picks.

Therefore, the equation becomes:

g ≤ 7

Next, to guarantee having at least one ball of each color, we need to take out 13 balls. So, from those 13 balls, we want at least 1 green ball and 1 red ball. This means the worst-case scenario is that we pick all the red balls in those 13 picks or all the green balls.

Therefore, the equation becomes:

r ≤ 13

Now, we can combine the equations to find the possible values for r and g:

g ≤ 7
r ≤ 13

Since we want to find the possible values, we take the maximum possible values for g and r.

g = 7
r = 13

So, there can be a maximum of 7 green balls and 13 red balls in the box to satisfy the given conditions.