Problem:
Five friends, Aurelio, Ennio, Flaminia, Lucia and Regolo, ate 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 euros to Caio" that must be carried out so that in the end each of the five has paid the same amount?
Pick one
Solution:
The answer is (C). The restaurant bill is 180 euros, the diners are 5, so each must pay 36 euros. Whoever advanced more than this amount must receive money from whoever advanced less (and in particular from the two friends who paid nothing). However, since no one must receive a multiple of the single share, there will necessarily be at least 4 transfers of money. A possible solution with 4 is the following:
Aurelio gives 36 euros to Flaminia.
Flaminia gives 72 (the 36 she received from Aurelio plus the 36 she owes) euros to Regolo,
Regolo gives 75 (the 72 he received from Flaminia plus the 3 he owes) euros to Ennio
who gives 54 of them to Lucia (the 75 he received from Regolo minus the 21 due to him).
At this point Lucia receives exactly the 54 due to her and each has paid their share.