1. Five friends, Aurelio, Ennio, Flaminia, Lucia, and Regolo, had dinner 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
1. The answer is (C). The restaurant bill is 180 euros, and there are 5 diners, so each person should pay 36 euros. Those who have paid more than this amount should receive money from those who have paid less (and in particular from the two friends who have not paid anything). However, since no one should receive a multiple of the individual share, there must be at least 4 money transfers. One possible solution with 4 transfers is as follows: Aurelio gives 36 euros to Flaminia. Flaminia gives 72 euros (the 36 she received from Aurelio plus the 36 she owes) to Regolo, Regolo gives 75 euros (the 72 he received from Flaminia plus the 3 he owes) to Ennio, who gives 54 euros to Lucia (the 75 he received from Regolo minus the 21 that are due to him). At this point, Lucia receives exactly the 54 euros that are due to her $(90-36=54)$, and everyone has paid their share.