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MathNet 2016-part-02 — 184 problems (EN–VI) Question 92

Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)

Question 92

Five friends, Aurelio, Ennio, Flaminia, Lucia and Regolo, had a meal at a restaurant. The bill is 180 euros, and it is paid by Lucia, Ennio and Regolo: the first pays 90 euros, the second 57 euros and the third 33 euros. What is the minimum number of transactions of the type "Tizio gives $n$ euros to Caio" that must be made so that in the end each of the five has paid the same amount?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6