Question 75
On planet $X$, 100 alien countries are in conflict. To avoid a world war, they form military alliances for mutual protection. The alliances obey these rules:
1) No alliance contains more than 50 countries.
2) Any two countries belong to at least one common alliance.
a) Can a country belong to fewer than three military alliances?
b) What is the minimum possible number of alliances satisfying both conditions?
1) No alliance contains more than 50 countries.
2) Any two countries belong to at least one common alliance.
a) Can a country belong to fewer than three military alliances?
b) What is the minimum possible number of alliances satisfying both conditions?