A card-board box contains 12 pairs each of three different types of hand gloves used by batsman 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?

Options

A. 3
B. 13
C. 25
D. 37

Explanation

To solve the problem of determining the minimum number of gloves one should take out to ensure getting at least one perfect pair, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have 12 pairs of gloves for three different types. This means there are a total of 36 gloves (12 pairs x 3 types).
- Each type has 12 left-hand gloves and 12 right-hand gloves.

2. **Worst-Case Scenario**:
- To ensure that we get at least one matching pair, we need to consider the worst-case scenario where we draw the maximum number of gloves without getting a pair.
- In the worst case, we could draw all gloves of one type first. For example, we could draw 12 left-hand gloves of type A and 12 right-hand gloves of type A, and then we could draw 12 left-hand gloves of type B.

3. **Calculating the Maximum Draws**:
- If we draw 12 gloves of type A (all left or all right), and then we draw 12 gloves of type B (again, all left or all right), we have now drawn 24 gloves without getting a pair.
- At this point, we could still be missing a glove from type C.

4. **Drawing the Next Glove**:
- When we draw the 25th glove, regardless of which glove we pick (left or right), it must match with one of the gloves we have already drawn. This is because there are only three types of gloves, and we have already drawn gloves from two types.

5. **Conclusion**:
- Therefore, to ensure that we have at least one perfect pair, we need to draw a minimum of **25 gloves**.

### Final Answer:
The minimum number of gloves one should take out to be sure of getting at least one perfect pair is **25 gloves**.