MathDB

In a football league, whenever a player is transferred from a team

X

with

x

players to a team

Y

with

y

players, the federation is paid

y-x

billions liras by

Y

y \geq x

, while the federation pays

x-y

billions liras to

X

x > y

. A player is allowed to change as many teams as he wishes during a season. Suppose that a season started with

18

teams of

20

players each. At the end of the season,

12

of the teams turn out to have again

20

players, while the remaining

6

teams end up with

16,16, 21, 22, 22, 23

players, respectively. What is the maximal amount the federation may have won during the season?

3