q32

Saumyojit

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There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

I got no idea as of NOW
 
There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

I got no idea as of NOW
Think of the worst case!

If you draw 5 pairs they could be all white

If you draw 11 shoes - those could be 10 white shoes and 1 black shoe.

If you draw 12 shoes - those could be 10 white shoes and 2 black Right shoe.


Continue......
 
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There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?
Once again you have been very lax in describing the question. There are seven pairs of black shoes. That means there are fourteen black shoes, seven for the left foot and seven for the right foot. Similarly for the five white pairs. But you have not said if any two black shoes, one right the other left form a matched pair. In other words are the shoes put in the box in matching pairs that are some how taped together. Or are the twenty-four shoes just a jumble of shoes all mixed-up together? In the latter case we could have one white left shoe and one white right shoe and still not have a matching pair. Please supply a correction if one is needed.
 
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There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?

I got no idea as of NOW
I would try to imagine the least likely scenario and then count the number of draws that guarantees its success
5 pairs of white shoes means 10 white shoes need to be drawn out.
7 left black shoes drawn out
1 right black shoe is drawn out completing the pair of black shoes.
Any of the remaining shoes would not change the result at this point if drawn.
To ensure drawing the pair of black shoes when repeating this test indefintely would have to at least account for this 'least likely scenario'
 
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