Multiple choice general knowledge math & puzzles

A woman has at least 2 pairs of black gloves, 2 pairs of white gloves, and 2 pairs of red gloves in a drawer. The gloves will fit either hand; they are not right or left-handed and each pair is identical. If they are removed from the drawer 1 at a time without looking at the colors, how many must she remove to be certain she has a matching pair for herself and her daughter?

  1. 7

  2. 6

  3. 9

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Worst-case scenario analysis: She could draw 1 black, 1 white, 1 red (3 gloves, no pair yet). Then she draws 2 more gloves in the same colors (e.g., 2 more black, making 2-1-1 or 2-2-1 distribution). At 5 gloves, she has only one complete pair. The 6th glove, regardless of color, will complete a second pair needed for both herself and her daughter. This is a pigeonhole principle problem.

AI explanation

To determine how many gloves the woman must remove to be certain she has a matching pair for herself and her daughter, we need to consider the worst-case scenario.

In this case, the worst-case scenario would be if she selects gloves of different colors each time. Therefore, she would need to remove gloves until she has at least one of each color. After that, the next glove she removes would guarantee a matching pair.

Let's go through each option to see which one is correct:

Option A) 7 - This option is incorrect because it assumes that the woman can have a matching pair after removing 7 gloves. However, it is possible that she could have selected gloves of all three colors (black, white, and red) without getting a matching pair.

Option B) 6 - This option is correct. If the woman removes 6 gloves, it is guaranteed that she will have at least one of each color. The next glove she removes would guarantee a matching pair.

Option C) 9 - This option is incorrect because it assumes that the woman needs to remove 9 gloves to have a matching pair. However, she could have selected gloves of all three colors (black, white, and red) before reaching 9 gloves.

Option D) 8 - This option is incorrect for the same reason as option C. It assumes that the woman needs to remove 8 gloves to have a matching pair, but she could have selected gloves of all three colors before reaching 8 gloves.

Therefore, the correct answer is B) 6.

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