Question 21
Emma purchased a bag of jellybeans, consisting of 15 blue, 9 green and 21 purple
jellybeans. She randomly grabs a handful of jellybeans from the bag. What is the
least number of jellybeans Emma must take to guarantee she has at least 12
jellybeans of the same colour?

To determine the least number of jellybeans Emma must take to guarantee she has at least 12 of the same color, we can use the Pigeonhole Principle. If we consider the worst-case scenario where she grabs jellybeans while trying to avoid getting 12 of any color, she could take 11 blue, 11 green, and 11 purple. That leads to:

11 (blue) + 11 (green) + 11 (purple) = 33 jellybeans.

However, on her next grab (the 34th jellybean), regardless of the color, she will inevitably have at least 12 jellybeans of one color. So the answer is 34 jellybeans!

In a situation where probabilities are at play, the Pigeonhole Principle is a useful concept that ensures outcomes in a seemingly random scenario by illustrating how grouping can lead to certainty in results. By understanding this principle, students can better strategize in problem-solving, not just in mathematics but in any situation requiring logical deduction!

Another fun fact is that jellybeans, originally made in the Middle East and inspired by Turkish delight, have been around since at least the 19th century. These delightful, chewy candies have become a staple in the candy world, with a huge variety of flavors, from classic fruit to bizarre novelty ingredients like buttered popcorn! Jellybeans are more than just a sweet treat; they carry a rich history that’s as colorful as their many hues!