Problem 18 · 2009 Math Kangaroo
Hard
Logic & Word Problems
off-by-onecareful-counting
Anna and Peter live in the same street. On one side of Anna’s house there are 27 houses, and on the other side 13 houses. Peter lives in the house right in the middle of the street. How many houses are there between Anna’s and Peter’s houses?
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Answer: A — 6
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Hint 1 of 2
Count all the houses: 27 on one side, Anna's own, and 13 on the other.
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Hint 2 of 2
Peter is the exact middle house; count the gap between his and Anna's positions.
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Approach: number the houses and locate Anna and Peter
- There are 27 + 1 + 13 = 41 houses, so the middle (Peter's) house is the 21st.
- Anna has 27 houses on one side, so she is the 28th house from that end.
- Houses strictly between the 21st and the 28th: 28 − 21 − 1 = 6.
- So there are 6 houses between them.
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