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 can not see the gloves from outside, but you can put your hands through the pigeon hole and takeout 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?
I'm not sure how the answer is 13.
Firstly, I think no of gloves are 24 since 12 pairs are there.
Now, to definitely make sure that we get a pair out, on the 1st attempt we take out 1 glove (23 gloves remain) and then on the next 22 attempts, I take out other gloves of different type (my assumption here is that the 1st glove I picked is of the type of which there are only 1 pair present) which would not match the glove I have already taken out. Now, on the next attempt 24th I will definitely take out the glove I want. Please explain why am I wrong here.
Thanks
Best Answer
The key here is
To "be sure" you have to account for the worst case scenario, which is that (however unlikely it is) you extract all (for example) right handed gloves first. Then you are sure that the next glove will be a left one, and will match any of the right gloves you have already extracted.
Since there are 12 pairs, the worst case scenario is that you extract 12 right hand gloves first. And then you are sure that the next one is going to be a left one, which will match one of the right handed gloves you have extracted first (because you have extracted all of them).
Any other scenario involves extracting less gloves, so 13 is the minimum to be sure.
In your example, there are 10 pairs of right-handed pairs of gloves, 1 left-handed pair and 1 keeping pair. In the worst case scenario, you pick for example 12 right hand gloves (10 right hands from the right-handed pairs, 1 right hand from the left-handed pair and 1 right hand from the keeper pair). Now the 13th glove must be a left hand glove, because there are no right hand gloves in the card-board box. It is either a left hand glove from one of the 10 right hand sets, the left hand glove from the left-handed set or the left hand glove from the keeper set.