Grace has 16 jellybeans in her pockets. She has 8 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
You just have to imagine the scenario that will cause her to take out the most jelly beans.
She could pick all the red ones, pick all the green ones, and then finally pick a blue one. You do the addition.
Oops... the MINIMUM. Sorry about that. (The above was for the maximum.)
She could pick a red, green, and blue right off the bat. Do the addition.
I'm officially insane. Ignore that. My original explanation is correct.
To find the minimum number of jellybeans Grace must take out of her pocket to ensure that she has one of each color, we need to consider the worst-case scenario.
Currently, Grace has 8 red jellybeans, 4 green jellybeans, and 4 blue jellybeans in her pockets. If she keeps taking jellybeans out randomly, the worst-case scenario would be if she keeps picking either red, green, or blue jellybeans without getting one of each color.
So let's consider this worst-case scenario:
1. Grace takes out the first jellybean; it could be red, green, or blue.
2. To prolong the worst-case scenario, let's assume she picks a red jellybean.
3. Now, she has 8 red jellybeans left, 4 green jellybeans, and 4 blue jellybeans.
4. The next jellybean she picks could still be red, prolonging the scenario further.
5. She keeps picking red jellybeans until none are left.
6. At this point, she needs to take out at least one more jellybean to guarantee she gets a different color.
7. Since all the remaining jellybeans are either green or blue, she needs to take at least one more jellybean, which would guarantee she gets a green or blue jellybean.
Therefore, in the worst-case scenario, Grace would need to take out a total of 8 (red) + 1 (for a different color) + 1 (green or blue) = 10 jellybeans.
So the minimum number of jellybeans Grace must take out of her pocket to ensure that she has one of each color is 10.