IOM 2017, Блиц — Задача 22

OLYMPIAD OF METROPOLISES. Moscow, September 4 · 4 септември 2017 г.

Условие

There are 20 lanes, numbered 1 to 20, and 4 runners called A, B, C, and D. The race organizers call a lane assignment optimal if there are at least 3 empty lanes between any two runners; i. e., whenever lanes $i$ and $j$ are assigned to some two runners, we have $|i-j| \ge 4$. (For example, the assignment of lanes 15, 1, 5, 20 to the runners A, B, C, D, respectively, is optimal.) How many optimal lane assignments are there?

Отговори

Решение

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