Problem 7 · 2009 Math Kangaroo
Medium
Logic & Word Problems
work-backwardsum-constraint
Sophie rolled a die four times and scored a total of 23 points. How many times did she roll a six?
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Answer: D — 3
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Hint 1 of 2
The biggest a single roll can be is 6.
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Hint 2 of 2
How close is 4 rolls of 6 to the total of 23?
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Approach: push the rolls to the maximum and see the gap
- Four rolls can total at most 4 × 6 = 24.
- She scored 23, which is just 1 less than 24.
- Dropping one roll from 6 to 5 loses exactly 1 point, so three rolls are 6 and one is 5.
- That means she rolled a six 3 times.
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