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2020 Math Kangaroo

Problem 10

Problem 10 · 2020 Math Kangaroo Medium
Logic & Word Problems careful-counting

A village of 12 houses has four straight streets and four circular streets. The map shows 11 houses. Each straight street has three houses, and each circular street also has three houses. Where should the 12th house be placed on this map?

Figure for Math Kangaroo 2020 Problem 10
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Answer: D — On D
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Hint 1 of 2
Each straight street needs 3 houses and each circular street needs 3 houses.
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Hint 2 of 2
Find the position where a street is currently one house short.
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Approach: check which street is missing a house
  1. Every street, straight or circular, must hold exactly three houses.
  2. Count the houses already on each street and find the one with only two.
  3. Placing the 12th house at spot D completes that street without overfilling any other.
  4. So the answer is D.
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