IOM 2020, Блиц — Задача 57

The Blitz-contest of IOM-2020

Условие

In a movie theater there are 4 VIP chairs labelled from 1 to 4. We call a few consecutive vacant chairs a block. In the online VIP seat reservation process the guest can choose in which block she wants to sit, and that if she wants to choose the first, last or middle seat (in case of a block of size even this means the middle chair with the smaller number). At some screening all VIP seats were reserved. In how many ways the reservation order could have happened?

For instance, if the seat 2 is reserved, then there are two blocks, one of them consists of the seat 1, the other one consists of the seats 3 and 4. Two reservation orders are different if there is a seat that was reserved in a different moment in the two orders.

Отговори

Решение

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Оригинал в Архива: iom-2020-blitz-tasks.pdf · официални решения: iom-2020-blitz-answers.pdf