November Puzzler - Digital Agent Blog
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November Puzzler

November Puzzler

Digital Agent engineers solve complex puzzles for our customers every day. Can you solve the Puzzle we created for you?

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

Hint: The best approach to this puzzle is logically, not via an equation.

Consider the worst-case scenario: we’ve taken out as many balls as possible so that no matter what ball we take next, we will have 7 of one color. This happens when we’ve taken out 6 green, 6 red, 6 blue, 6 yellow, 6 black, and 4 white. (The next ball we take will be either green, red, blue, or yellow, which will give us 7 of that color). This makes 6 + 6 + 6 + 6 + 6 + 4 + 1 = 35 the smallest number that guarantees at least 7 of the same color, since it is possible to draw 34 (6 + 6 + 6 + 6 + 6 + 4) or fewer balls and still not have 7 of any color.

“Impossible you are blindfolded – there is never a way.”  – Anonymous


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