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In a box there are red and blue balls. If you select a handful of them with eyes closed, you have to grab at least 5 5 of them to make sure at least one of them is red and you have to grab at least 10 10 of them to make sure both colors appear among the balls selected. How many balls are there in the box?

12 10 11 13 14

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1 solution

Paul Ryan Longhas
Feb 21, 2015

If 5 5 balls are needed to make sure at least one of them is red, that means that there are 4 4 blue balls in the box. If you need 10 10 to make sure both colors appear then there are 9 9 balls of the more used color –which must be red. Therefore there are 9 + 4 = 13 9 + 4 = 13 balls in the box.

Even though I got the question correctly, I think you have to edit the question. It is wrong as it is and does not conform to logic. Let me approach from a simple angle. If there are 13 balls in the box and there are 4 red balls, selecting a handful of five balls does not guarantee you will select a red ball. To do that, you'd need to select a handful of ten balls

Olawale Olayemi - 6 years, 3 months ago

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No there are 4 blue balls so yes selecting 5 balls would ensure that you get a red

Phillip Lambert - 6 years, 1 month ago

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Not if you grab 5 blue balls, which is entirely possible!

Amber Crownover - 5 years, 9 months ago

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@Amber Crownover Not if there are FOUR BLUE BALLS

Zoe Codrington - 2 years, 8 months ago

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