Problem 6 · 2013 Math Kangaroo
Easy
Counting & Probability
Logic & Word Problems
casework
A sack contains marbles in five different colours: 2 red, 3 blue, 10 white, 4 green and 3 black. You take marbles out of the bag without looking and without putting any back. What is the smallest number of marbles you must remove to be sure of having two of the same colour?
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Answer: E — 6
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Hint 1 of 2
Think about the worst luck possible while still avoiding a matching pair.
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Hint 2 of 2
This is a pigeonhole question: one of each colour first, then one more forces a repeat.
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Approach: pigeonhole / worst case
- There are 5 different colours, and every colour has at least two marbles.
- The worst case is drawing one marble of each colour: 5 marbles, all different.
- The very next marble (the 6th) must repeat a colour.
- So 6 marbles guarantee a matching pair.
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