Question

A cricket team has 10 blue pairs of gloves and 10 white pairs of gloves in a cricket kit. If a batter reaches into the kit and pulls out one glove at a time without looking at it, what is the least number of gloves she must pull out to make sure that she has a pair of gloves of the same colour?

Answer 1

Correct Answer: 21

To solve this problem, we need to determine the minimum number of gloves the batter must pull out to ensure she has a matching pair of the same color. We will use the pigeonhole principle, which can be applied in this context as follows:

1. There are two colors of gloves: blue and white.
2. The batter can encounter the worst-case scenario where every glove pulled out initially is a different color. In other words, she might pick one blue glove and one white glove, without forming a matching pair.
3. Now, consider the third glove. Regardless of its color, it must match with one of the two gloves already pulled out. This is because there are only two available colors, and she already has one glove of each color.

Therefore, the least number of gloves she must pull out to ensure at least one matching pair of the same color is 3.

Finally, verify the solution against the expected range (21, 21). The calculated value is 3, which does not fall within the expected range 21. However, the problem constraints and analysis show that 3 is indeed the correct solution based on the application of the pigeonhole principle.

The batter needs to pull out a minimum of 3 gloves to guarantee having a matching pair of the same color.