Mr. Blue has 12 brown gloves and 8 black gloves in a drawer in his closet. If he blindly pulls gloves from the drawer, what's the minimum number of gloves Mr. Blue will have to pick, to be certain he has a pair of gloves of the same color?
(In reply to
Answer by K Sengupta)
Mr. Blue has 12 brown(RW) gloves.
=> He has 6 pairs of RW gloves
Mr. Blue has 8 black(B) gloves.
=> He has 4 pairs of gloves.
Total no.of pairs of gloves possessed by Mr. Blue =6+4=10
Now, it is quite possible that Mr. Blue pulls 6 left-hand(lh) RW gloves and 4 lb RW gloves.
Other extreme possibilities are:
He pulls 6 right-hand(rh) RW gloves, 4 rh B gloves.
OR, he pulls 6 lh RW gloves, 4 rh B gloves.
OR, He pulls 6 rh-RW gloves, 4 lh gloves.
The possibilities regarding mixture of lh and rh RW gloves and lh/rh B gloves are not shown here.
In each of the extreme cases, Mr. Blue does not have a pair of gloves of the same colour.
He, therefore needs to pull 1 additional glove to satisfy the requirements Rs of the problem.
It can be easily verified that he will then have precisely ONE pair of gloves of the same colour.
Consequently, the required minimum number of gloves that Mr. Blue needs to pick is 11.
Edited on January 1, 2022, 4:25 am
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