Problem 4 · 2019 Math Kangaroo
Easy
Counting & Probability
careful-counting
How many different sums of the dots can one obtain if three ordinary dice are thrown at the same time?
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Answer: C — 16
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Hint 1 of 2
What is the smallest possible total of three dice? The largest?
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Hint 2 of 2
Every whole number from the minimum to the maximum is reachable, so just count them.
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Approach: count the range of attainable sums
- The smallest sum is 1+1+1 = 3; the largest is 6+6+6 = 18.
- Every integer from 3 to 18 can occur.
- That is 18 − 3 + 1 = 16 different sums.
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