Question

In a tournament with five teams, each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point, while the losing team scores zero. Which of the following is NOT necessarily true?

• A. There are at least two teams which have at most two points each
• B. There are at least two teams which have at least two points each
• C. There are at most three teams which have at least three points each
• D. There are at most four teams which have at most two points each

Answer 1

The correct option is D There are at most four teams which have at most two points each

Match Number	T1	T2	T3	T4	T5
1	1	0
2	1		0
3	0			1
4	0				1
5		1	0
6		1		0
7		0			1
8			1
9			1		0
10				1	0
Total	2	2	2	2	2

Let the teams be $T1,T2,T3,T4,T5$

According to the table each team can score atleast two points.

It contradicts our option $D$

So, option $D$ is correct