Find-tupple-natural-numbers-a-b-c-such-that-max-a-b-2-a-b-2-b-c-2-b-c-2-c-a-2-c-a-2-a-min-a-b-2-a-b-2-b-c-2-b-c-2-c-a-2-

Question Number 213459 by golsendro last updated on 06/Nov/24

Find tupple natural numbers (a, b, c)

such that

{\begin{cases} \max {\frac{a + b}{2} + \frac{∣ a - b ∣}{2}, \frac{b + c}{2} + \frac{∣ b - c ∣}{2}, \frac{c + a}{2} + \frac{∣ c - a ∣}{2}} = a \\ \min {\frac{a + b}{2} - \frac{∣ a - b ∣}{2}, \frac{b + c}{2} - \frac{∣ b - c ∣}{2}, \frac{c + a}{2} - \frac{∣ c - a ∣}{2}} = b \end{cases}

where a + b + c = 10