# Logical reasoning

#### Saumyojit

##### Full Member
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated; the team that remains undefeated in the second stage is declared the winner and claims the Gold Cup. The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.
What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?
a. 1
b. 2
c. 3
d. 4

I did this like this :
Suppose team A,B,C,D,E,F,G,H
A=5wins , 2 losses (Ag, Ah match)
B=5 wins, 2 losses (Bh, ba)
C= 5 wins , 2 losses (ca ,cb)
D= 4 wins, 3 losses (da, db, dc)
E=4 losees , 3 wins win=ef ,eg, eh matches
F= 5 losses , 2 wins win=fg , fh matches
G= 5 loss, 2 win Win= Ag, gh
H=5 loss , 2win Win= Ah, bh
Max 3 coming is it wrong or correct?

#### Saumyojit

##### Full Member
ok i found a solution which says

There are 28 matches in the 1st round, and hence 28 wins.
To find this, we have to assign maximum wins for 3 teams, and find the result for the 4th team. 1 team can win 7 matches, the next team a maximum of 6 matches, and the 3rd team can win a maximum of 5 matches. This means 18 wins for these 3 teams together.
There are 10 wins left, and 5 teams left. Hence, it is possible that each team can have 2 wins, and 1 out of this team can qualify for the next stage.

But mine apporach
was :

team A,B,C,D,E,F,G,H
A=5wins , 2 losses (Ag, Ah match)
B=5 wins, 2 losses (Bh, ba)
C= 5 wins , 2 losses (ca ,cb)
D= 4 wins, 3 losses (da, db, dc)
E=4 losees , 3 wins win=ef ,eg, eh matches
F= 5 losses , 2 wins win=fg , fh matches
G= 5 loss, 2 win Win= Ag, gh
H=5 loss , 2win Win= Ah, bh
Max 3 coming