Colored Balls

A bowl contains 50 colored balls: 13 green, 10 red, 9 blue, 8 yellow, 6 black, and 4 white. If you are blindfolded, what is the smallest number of balls you must pick to guarantee that you have at least 7 balls of the same color?
Source: NCTM Mathematics Teacher 2006

SOLUTION
It is like winning the lottery if you can pick out 7 balls of the same color one right after another. More likely you will pick the following balls (not in any particular order)
6 black (don’t want)
4 white (don’t want)
6 green (1 shy of 7)
6 red (1 shy of 7)
6 blue (1 shy of 7)
6 yellow (1 shy of 7)
Total = 34 balls
If you then pick one more ball (doesn’t matter what color), you will have 7 balls of the same color. 35 is the smallest number of balls you must pick to guarantee that you have at least 7 balls of the same color.

Answer: 35

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About mvtrinh

Retired high school math teacher.
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