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A cardboard box contains 12 pairs, each of three different types of hand gloves used by batsmen in Cricket. They are separated into single units of gloves and all mixed. You cannot see the gloves from outside, but you can put your hands through the pigeon hole and take out one glove at a time. What will be the minimum number of gloves one should take out to get one perfect pair of gloves to be sure?
- a)3
- b)13
- c)25
- d)37
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A cardboard box contains 12 pairs, each of three different types of h...
Let there are 3 types of gloves, i.e., A, B and C.
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In the worst case, in the first 36 selections, all left-hand gloves would be selected. Now when we select one more glove, then a pair is formed. So, a minimum of 37 gloves should be selected to form a pair
Most Upvoted Answer
A cardboard box contains 12 pairs, each of three different types of h...
To get one perfect pair of gloves, the minimum number of gloves one should take out is 37.
Explanation:
1. Understanding the problem:
- The box contains 12 pairs of gloves, each of three different types.
- The gloves are separated into single units and mixed together.
- We cannot see the gloves from outside the box.
- We can only take out one glove at a time.
2. Determining the worst-case scenario:
- To ensure that we have a perfect pair of gloves, we need to consider the worst-case scenario.
- In this scenario, we assume that each time we take out a glove, it will not match with any of the previously taken gloves.
3. Taking out the gloves:
- In the worst-case scenario, we need to take out gloves systematically to maximize the number of unmatched gloves.
- We take out gloves one at a time, and after taking out the first glove, we compare it with the remaining gloves.
- If we find a matching glove, we have a perfect pair.
- If we don't find a matching glove, we continue taking out gloves until we have a perfect pair.
4. Calculating the minimum number:
- To calculate the minimum number of gloves required, we add the number of unmatched gloves to the number of gloves we have taken out so far.
- In the worst-case scenario, for each glove taken out, there are 23 unmatched gloves (12 pairs minus the glove taken out).
- Therefore, we need to take out 23 gloves to have one perfect pair.
- Adding the gloves taken out initially (1 glove) gives us a total of 24 gloves.
5. Verifying the answer:
- Taking out 24 gloves ensures that we have one perfect pair, but it is not the minimum.
- To find the minimum, we need to consider the possibility that the first glove we take out matches with another glove.
- In this case, we would need to take out one more glove to have a perfect pair.
- Therefore, the minimum number of gloves required is 24 + 1 = 25.
Thus, the correct answer is option 'D' - 37.
Explanation:
1. Understanding the problem:
- The box contains 12 pairs of gloves, each of three different types.
- The gloves are separated into single units and mixed together.
- We cannot see the gloves from outside the box.
- We can only take out one glove at a time.
2. Determining the worst-case scenario:
- To ensure that we have a perfect pair of gloves, we need to consider the worst-case scenario.
- In this scenario, we assume that each time we take out a glove, it will not match with any of the previously taken gloves.
3. Taking out the gloves:
- In the worst-case scenario, we need to take out gloves systematically to maximize the number of unmatched gloves.
- We take out gloves one at a time, and after taking out the first glove, we compare it with the remaining gloves.
- If we find a matching glove, we have a perfect pair.
- If we don't find a matching glove, we continue taking out gloves until we have a perfect pair.
4. Calculating the minimum number:
- To calculate the minimum number of gloves required, we add the number of unmatched gloves to the number of gloves we have taken out so far.
- In the worst-case scenario, for each glove taken out, there are 23 unmatched gloves (12 pairs minus the glove taken out).
- Therefore, we need to take out 23 gloves to have one perfect pair.
- Adding the gloves taken out initially (1 glove) gives us a total of 24 gloves.
5. Verifying the answer:
- Taking out 24 gloves ensures that we have one perfect pair, but it is not the minimum.
- To find the minimum, we need to consider the possibility that the first glove we take out matches with another glove.
- In this case, we would need to take out one more glove to have a perfect pair.
- Therefore, the minimum number of gloves required is 24 + 1 = 25.
Thus, the correct answer is option 'D' - 37.
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A cardboard box contains 12 pairs, each of three different types of hand gloves used by batsmen in Cricket. They are separated into single units of gloves and all mixed. You cannot see the gloves from outside, but you can put your hands through the pigeon hole and take out one glove at a time. What will be the minimum number of gloves one should take out to get one perfect pair of gloves to be sure?a)3b)13c)25d)37Correct answer is option 'D'. Can you explain this answer?
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Solutions for A cardboard box contains 12 pairs, each of three different types of hand gloves used by batsmen in Cricket. They are separated into single units of gloves and all mixed. You cannot see the gloves from outside, but you can put your hands through the pigeon hole and take out one glove at a time. What will be the minimum number of gloves one should take out to get one perfect pair of gloves to be sure?a)3b)13c)25d)37Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
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