Problem 12 · 2025 Math Kangaroo
Medium
Logic & Word Problems
sum-constraintextremal
17 squirrels are sitting on 4 trees. There are at least 2 squirrels on each tree. The number of squirrels is different on each tree. What is the largest possible number of squirrels on one tree?
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Answer: B — 8
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Hint 1 of 3
To put as many squirrels as possible on one tree, leave as few as possible on the others.
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Hint 2 of 3
The other three trees still need at least 2 each, and all four numbers must be different.
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Hint 3 of 3
The three smallest different numbers, each at least 2, are 2, 3 and 4.
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Approach: minimise the other three to maximise one
- Each tree needs at least 2 squirrels and all four counts are different.
- Make three trees as small as possible: 2, 3 and 4 squirrels.
- Those three trees hold 2 + 3 + 4 = 9 squirrels, leaving 17 − 9 = 8 on the last tree. The answer is B.
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