Problem 2 · 2015 Math Kangaroo
Easy
Algebra & Patterns
off-by-one
After mum had hung the t-shirts on the washing line for drying, her son hung a single sock between each two t-shirts. Now there are 29 pieces of clothing on the line. How many of them are t-shirts?
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Answer: E — 15
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Hint 1 of 2
A sock goes in every gap between two t-shirts, so socks number one fewer than t-shirts.
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Hint 2 of 2
If there are T t-shirts, the line holds T + (T−1) pieces; set that equal to 29.
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Approach: count gaps between items
- With T t-shirts there are T−1 gaps, so T−1 socks.
- Total pieces: T + (T−1) = 2T − 1 = 29.
- So 2T = 30 and T = 15.
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