Y by ys-lg, lkjin7932
For a competition a school wants to nominate a team of
students, where
is a given positive integer. Each member of the team has to compete in the three disciplines juggling, singing and mental arithmetic. To qualify for the team, the
students of the school compete in qualifying competitions, determining a unique ranking in each of the three disciplines. The school now wants to nominate a team satisfying the following condition:
If a student
is not nominated for the team, there is a student
on the team who defeated
in at least two disciplines.
Determine all positive integers
such that for any combination of rankings, a team can be chosen to satisfy the condition
, when
a)
,
b)
.







Determine all positive integers


a)

b)
