$\left.\begin{array}{l}{[\text { Order relation }} \\ {[\text { Pigeonhole Principle (other). }]}\end{array}\right]$

Four friends came to the ice rink, each with her brother. They paired up and started skating.

It turned out that in each pair the "escort" was taller than the "lady" and no one was skating with their sister. The tallest in the group was Yura Vorobyov, followed by Andrey Egorov, then Lusya Egorova, Seryozha Petrov, Olya Petrova, Dima Krymov, Inna Krymov, and Anya Vorobyova. Determine who skated with whom.
With whom does Lusya Egorova, the tallest among the girls, skate?

## Solution

The tallest girl is Lusya Egorova, and according to the condition, she skates with a boy who is taller than her. There are two such boys, but one of them is her brother. Therefore, Lusya Egorova skates with Yura Vorobyov. Reasoning similarly, we establish that Olya Petrova skates with Andrey Egorov, Inna Krymova with Seryozha Petrov, and Anya Vorobyova with Dima Krymov.

## Answer

Lusya Egorova and Yura Vorobyov, Olya Petrova and Andrey Egorov, Inna Krymova and Seryozha Petrov, Anya Vorobyova and Dima Krymov.