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ONM 2010 Calarasi Problema 4

 
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Andi Brojbeanu
Newton


Joined: 22 Mar 2009
Posts: 383
Location: Targoviste (Dambovita)

PostPosted: Sat May 29, 2010 10:28 pm    Post subject: ONM 2010 Calarasi Problema 4 Reply with quote

In doua tari vecine, Narnia si Urania, unitatile monetare sunt reprezentate de monede numite taleri, respectiv arginti. In Narnia un argint se schimba cu 4 taleri si in Urania un taler se schimba cu 9 arginti. Miraz trece dintr-o tara in alta si schimba monede. Initial Miraz se afla in Narnia si are un singur taler si niciun argint.
a) Veri cati daca la un moment dat Miraz poate avea in total 21 de monede.
b) Demonstrati ca in niciun moment Miraz nu poate avea numarul de taleri egal cu numarul de arginti.
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Brojbeanu Andi Gabriel, clasa XII-a
Colegiul National "Constantin Carabella" Targoviste
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