In a jar there are 21 white balls, 24 green balls and 32

Question

In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?

a) 23
b) 46
c) 57
d) 66
e) 67

Bunuel · Accepted Answer

To ensure that we have 23 balls of the same color, we should consider the worst case scenario. The worst case scenario would be if we take 21 white balls, 22 green balls and 22 blue balls. In this case we won't have 23 balls of the same color. After that, there will be only green and blue balls left in the jar and no matter which one we take next we'll have either 23 green or 23 blue balls. So, the minimum number of balls we should pick is 21 + 22 + 22 + 1 = 66. Answer: D. Similar questions to practice: 12-easy-pieces-or-not-126366.html#p1033935 in-his-pocket-a-boy-has-3-red-marbles-4-blue-marbles-and-85216.html of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html in-a-deck-of-52-cards-each-card-is-one-of-4-different-color-83183.html a-box-contains-10-red-pills-5-blue-pills-12-yellow-56779.html each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html a-student-is-asked-to-pick-marbles-from-a-bag-that-contains-72390.html of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html if-a-librarian-randomly-removes-science-books-from-a-library-93861.html each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html a-box-contains-10-tablets-of-medicine-a-and-15-tablets-157726.html there-are-12-red-balls-10-blue-balls-15-red-balls-and-134437.html Hope it helps.

Gnpth · Answer

Here, we need to find minimum number of marbles to be taken out to get 23 marbles of same color.

For a instance, if we take 21 white marbles 1st and followed by 22 Green and then 22 Blue.

Total will be 21 + 22+ 22= 65 draws.

If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 23.

So Minimum we need to take 65+1 = 66 Times to get 23 marbles of same color(either Green or Blue).

Answer : D.

Hope it helps.

himanshujovi · Answer

I think the trick is in the scope shifting so 23 of one colour can be either in the jar by removing other marbles or outside the jar as a result of being moved out.

dstephens · Answer

The answer is 23.

Remember? The balls are in a jar. Jars are made of glass so you can see the colors of the ones that you wanted to take out.

mvictor · Answer

very tricky, and the wording is confusing.

23 of the same color must be left in the jar or outside?
if in the jar, then we need to take at least 21 out + 1 green and 32 blue or 21 white 24 green and 9 blue. but neither works, so it must be the case that we need to take out, and see if we have at least 23 of the same kind.
to make sure that we have 23 of the same kind, we need to take 21 white, 23 blue or green and 22 blue or green. this gives us a total of 66.
what is the source of this question?

KarishmaB · Answer

Actually, the wording of the question is quite standard. How many do you need to take out to ensure that you have 23 of the same colour? means that out of the balls taken out, we need to ensure that there should be 23 of the same colour.

AkshdeepS · Answer

VeritasKarishma : Not able to understand what the question is asking and how to imagine this situation of marbles.

Please help.

KarishmaB · Answer

Think about a simpler case. 
Say you have a box with 2 red balls, 2 blue balls and 2 white balls. Now you need to take out some balls to ensure you have two fo the same colour. How many balls do you need to take out to ENSURE that you have 2 balls of same colour. 
Say, you took out a red ball. Then a blue ball. Then a white ball. You still don't have 2 balls of same colour. Now the next ball you take out will make it two balls of same colour. So we need to take out 4 balls to ENSURE that there are 2 of the same colour.

This is the same case here. Now, review the original question and solution.

kunalbean · Answer

Hi! Can you please explain that why are we taking only 22 marbles for Green? The worst case scenario will be when last 3 are of different color and the one we pick will result in all of same color. Hence, 21+23+23 - 3 + 1 = 65.

sanjayparihar16 · Answer

We are taking only 22 marbles for Green  because 1 more marble would suffice our need i.e. 23 marbles of same colour. So we are trying to reach a case where we are just one short of a marble such that any marble pick would help in reaching the required condition.

Crytiocanalyst · Answer

To make sure we have 23 balls of the colour we have to adapt the pigeon hole stratergy

Take the number just below the given number that makes up these balls the number being 22

so that 21 balls from the first jar 22 from jar 2 and 3 respectively

and finally adding 1 ball just to make it 1 colour of 23

Therefore total =21+22*2+1= 66 hence D

bumpbot · Answer

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In a jar there are 21 white balls, 24 green balls and 32

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