If you have a box of crayons with three shades of green, four shades of red, sixteen shades of blue and thirteen of yellow, how many do you have to pull out to guarantee that you get four of the same colour?
To guarantee that you get four of the same color, you need to know the minimum number of crayons you would need to pull out to ensure this condition.
To start, let's determine the worst-case scenario. You want to have four crayons of the same color. This means you would need to pull out three crayons of each color, except for one. In that case, you would still not have four of the same color.
Let's calculate based on this worst-case scenario.
There are three shades of green, four shades of red, sixteen shades of blue, and thirteen shades of yellow.
So, if we pick three crayons of each of the three colors, then we have a total of 3 x 3 = 9 crayons.
Next, we pick three crayons of blue and three crayons of yellow, adding another 3 + 3 = 6 crayons.
Adding all of these, we have 9 + 6 = 15 crayons chosen.
At this point, we still do not have four crayons of the same color because we have only taken three shades of green.
Finally, we need to pick one additional crayon, which would mean we have chosen 15 + 1 = 16 crayons in total.
Therefore, you have to pull out a minimum of 16 crayons to guarantee that you get four of the same color from the given box.