# Who won against Whom

Five teams from five different colleges- S, K, M, V and N, participated in Champions League (ICCL) played in the year 2008. Each team played exactly one match against every other team. But due to some virus, data was corrupted and it was all up to the memory based facts remembered by statisticians. These facts are listed below. Each win provides two points to the winning team, each No-Result (i.e. N/R) gains one point to both teams and a loss gains zero. If two teams score same points, the team with higher run rate gets higher rank.

1. The performance chart (number of won-Lost-N/R matches) for only S and K was identical. S topped the list because of the higher net run rate.
2. N didn’t win any match.
3. M won two matches and lost one.
4. There was only one match which didn’t produce any result. Every team scored at least one point.
5. V beat only N.

What were the results of the 10 matches?

Source : time.com

N had to participate in the N/R match, otherwise it couldn't get any points. Neither S nor K could be the other team in the N/R match, otherwise it would make their performance charts differ. V couldn't be it either, since 5 says it beat N. Thus, N/R match was between N and M, and N lost the rest of its matches.

Now, V team

lost all matches except with N, and had no N/Rs.

For teams S, K and M,

each of them won one of their matches with the other two teams and lost the other. I don't think there is any information to disambiguate between the cases.

So there are two possible values for the results (italics highlight differences):

S won against K, V and N and lost to M; K won against M, V and N and lost to S; M won against S and V, lost to K and tied with N; V won against N and lost to S, K and M; N tied with M and lost to S, K and V,

or

S won against M, V and N and lost to K; K won against S, V and N and lost to M; M won against K and V, lost to S and tied with N; V won against N and lost to S, K and M; N tied with M and lost to S, K and V.

• Thanks @Mariia Mykhailova. Can you tell why you started with N/R match clue?
– sam
Oct 11, 2018 at 14:09
• Because it was the only special event in the matches, and it was obvious that clues 2 and 4 together will allow to identify it immediately. Oct 11, 2018 at 15:45