MathDB

Before The World Cup tournament, the football coach of

F

country will let seven players,

A_1, A_2, \ldots, A_7

, join three training matches (90 minutes each) in order to assess them. Suppose, at any moment during a match, one and only one of them enters the field, and the total time (which is measured in minutes) on the field for each one of

A_1, A_2, A_3

, and

A_4

is divisible by

7

and the total time for each of

A_5, A_6

, and

A_7

is divisible by

13

. If there is no restriction about the number of substitutions of players during each match, then how many possible cases are there within the total time for every player on the field?

Problem Statement