Problem 10 · 2017 Math Kangaroo
Easy
Logic & Word Problems
off-by-one
Some girls are standing in a circle. The teacher makes them do a headcount: Bianca says one, her neighbour says two, and so on. If they count in a clockwise direction, Antonia says five. If they count in an anticlockwise direction, Antonia says eight. How many girls are forming the circle?
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Answer: C — 11
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Hint 1 of 2
Count the gaps between Bianca and Antonia going each way around the circle.
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Hint 2 of 2
The two arcs together make one full loop.
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Approach: add the two arc lengths
- Clockwise, Antonia is the 5th, so 4 girls separate them that way.
- Anticlockwise she is the 8th, so 7 girls separate them the other way.
- Around the whole circle: 4 + 7 = 11 girls.
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