There are 10 black, 10 red, 10 green, 10 blue, and 10 white marbles.
What is the minimum number of marbles that you would have to take out of the box in order to be certain that you would have drawn out three marbles of the same color? Why?
11.
The most that you could take out without drawing three is two of each color which makes
black red green blue white total
2 + 2 + 2 + 2 + 2 = 10
So drawing 1 more marble will ensure that the next marble will be the third of one of those five colors.
Another argument might be that if the box is transparent you can easily see and chose 3 marbles of the same color in 3 draws.
September 30th, 2009 at 12:47 pm
I’ve seen lots of variations of this old puzzle over the years. The answer is 11.
Think of the unluckiest possible scenario:
You first draw 5 marbles. NONE of them match.
Then you end up drawing one black, one red, one green, one blue, and one white. Now you have a total of 10 marbles, made up of 2 of each of the 5 colors. No set of 3 marbles are all the same color.
But when you draw an 11th marble, it doesn’t matter what color it is, because it must match one of the existing pairs you have. So drawing 11 marbles will guarantee that you have at least 3 of the same color.
Of course you could get lucky and pick 3 marbles of the same color on your first try. Or maybe after taking 11 marbles, you have a few trios of matching marbles. But there’s no guarantee that either of these things will happen. You need to take 11 marbles to get at least one matching set of 3.
References :
September 30th, 2009 at 1:23 pm
11.
The most that you could take out without drawing three is two of each color which makes
black red green blue white total
2 + 2 + 2 + 2 + 2 = 10
So drawing 1 more marble will ensure that the next marble will be the third of one of those five colors.
Another argument might be that if the box is transparent you can easily see and chose 3 marbles of the same color in 3 draws.
References :
September 30th, 2009 at 1:48 pm
11
References :