IOM 2016, Блиц — Задача 55

Olympiad of Metropolises, Moscow. Blitz Contest, September, 5 · 5 септември 2016 г.

Условие

Let $\mathcal{R}$ be the set of all triples $(x, y, z)$ of non-negative integers such that $x + y + z = 100$ and at least one of two conditions holds: $x \ge 28$ or $z \ge 42$.

For example, one such triple is $(27, 12, 61)$.

How many elements does set $\mathcal{R}$ have?

Решение

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Оригинал в Архива: blitz.pdf