Thursday, February 25, 2010
Glove selection
There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow, and 2 pairs of green. You select the gloves in the dark and can check them only after a selection has been made. What is the smallest number of gloves you need to select to have at least one matching pair in the best case? in the worst case?
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Best case is 2 if you're lucky and 11 if you are unlucky enough to get all 10 red ones in one hit
ReplyDeleteIn the best case, you select 2 gloves and their are identical.
ReplyDeleteIn the worst case, you should select 4 gloves, in this case, you will have at least one pair.
Because if you got 1 red, 1 blue and 1 yellow, the 4th will be red or blue or yellow... you have your pair!
best case 2
ReplyDeleteworst case 4
YEA...TRUE ITS 2 AND 4.
ReplyDeleteworst case is 11.
ReplyDeleteYou pick any glove for the left hand.
So we now have one glove.
Let us consider it is blue.
On the right hand we can get 5 red and 4 yellow in any order.
WE now have 10 gloves. 1blue for left hand, 5 red and 4 white for right hand.
Next should be a blue glove for the right hand which makes it a pair.
So the 11th glove makes the right pair for the worst case.
worst case is 12
ReplyDeletethe first 11 gloves may be all left handed.. but 12th one will surely match one of the 11 previously selected... making a pair
absoutly correct
Deletehowever best case is 2 but worst case according to me here pegion hole principle can be applied and smallest no.to make sure that it is to select 8 pairs .
ReplyDelete