Problem 4 · 2011 Math Kangaroo
Easy
Number Theory
careful-counting
In Crazytown the houses on the right-hand side of the street all have odd numbers. The Crazytowners don't use any numbers with the digit 3 in them. The first house on the right-hand side has the number 1. Which number does the fifteenth house on the right-hand side have?
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Answer: E — 47
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Hint 1 of 2
List the odd house numbers in order, but skip any that contain the digit 3.
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Hint 2 of 2
Count carefully until you reach the 15th allowed number.
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Approach: list allowed odd numbers and count to the 15th
- Odd numbers with no digit 3, in order: 1, 5, 7, 9, 11, 15, 17, 19, 21, 25, 27, 29, 41, 45, 47.
- (We skip 3, 13, 23, and 31–39 because they contain a 3.)
- The 15th number in this list is 47.
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