MEMO 2018 ekipno problem 3

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Dodao/la: arhiva
Sept. 8, 2018

A group of pirates had an argument and now each of them holds some other two at gunpoint. All the pirates are called one by one in some order. If the called pirate is still alive, he shoots both pirates he is aiming at (some of whom might already be dead). All shots are immediately lethal. After all the pirates have been called, it turns out that exactly 28 pirates have been killed.

Prove that if the pirates have been called in whatever other order, at least 10 pirates would have been killed anyway.

Source: Srednjoeuropska matematička olimpijada 2018, ekipno natjecanje, problem 3