Problem 26 · 2023 Math Kangaroo
Stretch
Logic & Word Problems
Arithmetic & Operations
work-backwardsum-constraint
Several mice live in three houses. Last night every mouse left its house and moved directly to one of the other two houses. The diagram shows how many mice were in each house yesterday (“gestern”) and today (“heute”). How many mice used the path indicated by the arrow?
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Answer: B — 11
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Hint 1 of 2
Every mouse leaves its own house, so each house's outgoing mice split between the other two.
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Hint 2 of 2
Set up the flows between the three houses from yesterday's and today's counts; the arrow is one of those flows.
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Approach: balance the mouse flows between the three houses
- Yesterday the houses held 8, 7, 5 and today they hold 6, 10, 4; every mouse moved to a different house.
- Writing the six directed flows and using that each house empties out gives equations linking them.
- Solving for the arrowed flow yields 11 mice.
- So the answer is 11 (B).
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