Problem 7 · 2018 Math Kangaroo
Medium
Counting & Probability
careful-counting
How many times do you have to roll an ordinary die to be certain that at least one number is rolled twice?
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Answer: C — 7
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Hint 1 of 2
Think about the worst possible luck: how many different results could you get with no repeat at all?
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Hint 2 of 2
A die has 6 faces, so after 6 all-different rolls the very next roll must repeat one (pigeonhole).
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Approach: pigeonhole / worst case
- A die shows only 6 different numbers.
- In the unluckiest case the first 6 rolls are all different, one of each number.
- The 7th roll has to match a number already seen.
- So 7 rolls make a repeat certain.
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