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2017 Math Kangaroo

Problem 19

Problem 19 · 2017 Math Kangaroo Stretch
Logic & Word Problems caseworksum-constraint

Four brothers have eaten 11 biscuits altogether. Everyone has eaten at least one biscuit but all of them have eaten a different amount of biscuits. Three of the brothers ate 9 biscuits altogether, where one of them got exactly 3 biscuits. How many biscuits did the boy who had the most biscuits eat?

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Answer: C — 5
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Hint 1 of 2
First find how many the fourth brother ate, then split the other 9 among three different amounts.
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Hint 2 of 2
All four numbers are different and at least 1; one of the trio is exactly 3.
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Approach: find the outsider's count, then fill the trio with distinct values
  1. Three brothers ate 9, so the fourth ate 11 - 9 = 2.
  2. The trio (summing to 9) includes a 3, so the other two add to 6.
  3. They must be different from each other and from 2 and 3, so they are 1 and 5.
  4. The most any brother ate is 5.
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