Posted by Cyndie on .
Say that a bag contains 100 marbles: 30 red, 30 blue, 30 green, plus a mix of 10 yellow and orange marbles. To be certain that you have 10 marbles of the same color, what is the minimum number you would need to remove (without looking) from the bag?
Since there are 3 colors with more than 10 marbles, you'd need 3*9+1 = 28 marbles to ensure that 10 are the same color (red,blue,green). Add to that the other 10 which are just nuisance marbles (since you can't ever get 10 orange or yellows), and you have 38 marbles.
Once you have drawn 27, you might have 9 each of red,blue,green. If you then draw all the yellows and oranges, you have taken 37 marbles. The next marble must be red,green, or blue.