Problem 18 · 2014 Math Kangaroo
Stretch
Logic & Word Problems
casework
Seven children stand in a circle. Nowhere are two boys standing next to each other. Nowhere are three girls standing next to each other. What is possible for the number of girls? The number of girls can…
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Answer: C — …only be 4.
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Hint 1 of 3
Try drawing 7 dots in a ring and colouring some as boys (B) and some as girls (G).
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Hint 2 of 3
No two B's may touch, and no run of three G's is allowed, so the boys must spread out to break up the girls.
Still stuck? Show hint 3 →
Hint 3 of 3
See how many boys you must have, then the rest are girls.
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Approach: place boys to keep girls in short runs, and count what is left
- Since no two boys may stand together, the boys must be spaced apart around the ring of 7.
- If there were only 2 boys, the other 5 girls would have to bunch up and three girls would end up together, which is not allowed.
- So we need 3 boys spread out, breaking the 7 children into girl-runs of at most two; that leaves exactly 4 girls (like B G G B G G B around the ring).
- The number of girls can only be 4.
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