Multiple choice general knowledge science & technology

• Mr. Brown has 6 black gloves and 12 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color?

  1. 7

  2. 3

  3. 13

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mr. Brown has 6 black gloves and 12 brown gloves (18 total, 2 colors). Worst case: picking 1 glove of each color gives no pair. With only 2 colors available, by the pigeonhole principle, picking 3 gloves guarantees at least 2 are same color (either 2 black or 2 brown). This works regardless of specific quantities - you only need to know there are 2 colors.

AI explanation

To answer this question, we need to consider the worst-case scenario.

Let's assume that Mr. Brown picks gloves in such a way that he always selects gloves of a different color than the ones he has already picked. In this scenario, he would need to pick the maximum number of gloves without finding a matching pair.

Mr. Brown has 6 black gloves and 12 brown gloves. Since he wants to find a pair of the same color, he needs to pick the maximum number of gloves without finding a pair.

In the worst-case scenario, Mr. Brown would first pick a black glove, then a brown glove, then another black glove. At this point, he still does not have a pair of gloves of the same color.

Therefore, the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color is 3.

Option B) 3 - This option is correct because in the worst-case scenario, Mr. Brown will need to pick at least 3 gloves to find a pair of gloves of the same color.

The correct answer is B) 3.

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