Problem 7 · 2011 Math Kangaroo
Medium
Logic & Word Problems
off-by-one
The 17 houses in my street are numbered consecutively, on one side with the odd numbers 1, 3, 5,… and on the other side with the numbers 2, 4, 6,…. My house is the last one on the even side and has the number 12. Yours is the last one on the odd side. Which number does your house have?
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Answer: E — 21
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Hint 1 of 2
First figure out how many houses are on the even side, given the largest even number is 12.
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Hint 2 of 2
The rest are on the odd side; find the last (largest) odd number there.
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Approach: split the 17 houses across the two sides
- My house is the last even number, 12, so the even side has 2,4,6,8,10,12 — that is 6 houses.
- The other 17−6 = 11 houses are on the odd side.
- The 11th odd number is 21, so your house is number 21.
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