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2009 Math Kangaroo

Problem 15

Problem 15 · 2009 Math Kangaroo Hard
Logic & Word Problems caseworksum-constraint

Three squirrels Anni, Asia and Elli have collected 7 nuts. They have all collected a different amount of nuts, and everybody has collected at least one nut. Anni has collected the least and Asia the most. How many nuts has Elli collected?

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Answer: B — 2
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Hint 1 of 2
All three counts are different whole numbers, each at least 1, adding to 7.
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Hint 2 of 2
With Anni smallest and Asia largest, try the smallest possible values for Anni.
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Approach: find the only set of three distinct positive numbers summing to 7
  1. The three counts are different and each at least 1, with Anni least and Asia most.
  2. The smallest Anni can be is 1; the three must still differ and sum to 7.
  3. 1 + 2 + 4 = 7 is the only way, so Anni = 1, Elli = 2, Asia = 4.
  4. Elli collected 2 nuts.
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