Problem 6 · 2017 Math Kangaroo
Medium
Logic & Word Problems
Arithmetic & Operations
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 six. If they count in an anticlockwise direction, Antonia says nine. How many girls are forming the circle?
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Answer: C — 13
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Hint 1 of 2
Count the gap from Bianca to Antonia each way around the circle.
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Hint 2 of 2
Going clockwise and anticlockwise covers the whole circle once.
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Approach: add the two arc-gaps to get the total around the circle
- Clockwise, Antonia is number 6, so she is 5 girls along from Bianca.
- Anticlockwise she is number 9, so she is 8 girls along the other way.
- The two arcs together go right round the circle: 5 + 8 = 13 girls, choice C.
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