Marbles in a Box

Logic Level 1

A box has 26 marbles. 6 are red, 3 are green, 10 are purple and 7 are orange. Rachel takes the marbles out one by one without looking into the box. What is the fewest number of marbles she must take out to be certain at least 3 of them are purple?


The answer is 19.

Isabelle Hsu by Isabelle Hsu , 16, Hong Kong

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3 solutions

Noam Amozeg
Jan 29, 2019

In a worst-case scenario, all of the marbles she draws won't be purple until purple is the only color left in the box. Therfore, to be completely certain that she will draw at least 3 purple marbles, she first has to draw the amount of all other colored marbles. Drawing 6 red, 3 green, and 7 orange marbles gets a total of 16 marbles that aren't purple. Drawing three more (which have to be purple in this worst-case scenario) gets the total marbles drawn to 19.

2 Helpful 0 Interesting 1 Brilliant 0 Confused
Addie Mendelson
Jan 30, 2019

You could pull out 6 red first, then 3 green, then 7 orange and that adds up to 16, but you still don't have any purple marbles. So the next 3 you pull out will be guaranteed to be purple. You add up 16+3=19. The answer is 19 Good Job!!! 👍

1 Helpful 0 Interesting 1 Brilliant 0 Confused
Isabelle Hsu
Jan 31, 2019

You have to think about the worst case scenario, which is not getting any purple until the end. 6 red, 3 green, 7 orange. So there is only purples left in the box. The next 3 are guaranteed to be purples. You add up 6+3+7+3. The answer is 19. 🙃

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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