Problem 2 · 2023 Math Kangaroo
Easy
Counting & Probability
sum-constraintcasework
Julia rolls 5 dice at the same time. She obtains a sum total of 19 points. What is the biggest number of sixes she can have rolled?
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Answer: C — 2
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Hint 1 of 2
If she rolled k sixes, the other 5−k dice are each at least 1.
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Hint 2 of 2
Test the largest k whose minimum total still fits under 19.
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Approach: check the largest feasible number of sixes
- Three sixes give 18; the remaining two dice add at least 2, for at least 20 — too much.
- Two sixes give 12; the remaining three dice must total 7, which is possible (e.g. 1+2+4).
- So the most sixes she can have is 2.
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