Summer camp

Task number: 3919

There are 15 children in the summer camp, three children have a service in the kitchen every day, and each pair of children has exactly one common service. How many days does the camp last?

  • Solution

    In two ways, we count the number of pairs of children who served together.

    \(\# \text{pairs} = \binom{15}{2}\), because there are so many pairs of children.

    \(\# \text{pairs} = \#\text{days} \cdot \binom{3}{2}\), because on evey service \(\binom{3}{2}\) pairs meet.

    Hence \(\#\text{days} = \frac{\binom{15}{2}}{\binom{3}{2}}=35\).

  • Answer

    The camp lasts 35 days.

Difficulty level: Easy task (using definitions and simple reasoning)
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