Problem 8.4. Thirty-six children are standing in a circle, each dressed in a red or blue sweater. It is known that next to each boy stands a girl, and next to each girl stands a person in a blue sweater. Find the maximum possible number of girls in red sweaters.

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# Answer: 24.

Solution. Note that there will not be 3 girls in red sweaters standing in a row (otherwise, the condition would not be satisfied for the middle one). By dividing 36 children into 12 triplets, we get that in each of them there are no more than 2 girls in red sweaters, and the total number of girls in red sweaters is no more than \(2 \cdot 12 = 24\).

![](https://cdn.mathpix.com/cropped/2024_05_06_b135fe79f2e6ed0cbffag-3.jpg?height=492&width=523&top_left_y=89&top_left_x=465)

Fig. 6: to the solution of problem 8.4

It is easy to construct an example: in each of the 12 triplets, two girls in red sweaters are arranged clockwise, followed by a boy in a blue sweater (Fig. 6). It is clear that all the conditions of the problem are satisfied.