# Games and Tournaments - Questions and Answers

In this topic, a scenario is given based on games/ sports/ tournaments and from given scenario questions are asked.

Sometimes a tabular format is given with some blank cells in it, and by observing the table and from the given scenario we have to first fill all the missing values in the table and then we have to solve the questions.
But the most common questions from this chapter are the ones we are covering below.

## Importance of topic

These types of questions are asked in CAT and other such high level exams.

## Key Points

• If G, H and I is your answer and options are G and H, H and I, G and I and "None of the above" then you should mark "None of the above".

• M lost to N but won against O and P means M won against O and P.

• M lost to N who in turn won against O and P means N won against O and P.

• If it is given that "M did not win against N" then it does not necessarily mean that N won. In such a case draw/ tie is a possible conclusion.

• Standing are the positions (Like position in point table) of a team after completion of a round/ part of tournament.

• If you have taken more than 5 minutes to read and draw a possible table/ format and you are still not getting clean data then you must leave that question and move on to the next problem, because sometimes overlooking on a data point results into getting stuck in the sets. So take a break from that question and then approach these questions again afresh.

• Knock-out matches are those in which loser exits from the tournament.

• In a knock-out tournament, if n number of teams or n number of players is given then total n-1 number of matches is played. Also, in case of "Bye" system this logic is true.
For example, If there are 10 teams in a knock-out tournament then there should be 9 (i.e. 10 - 1 (n - 1)) matches played.

• Round-Robin tournaments are those in which each team has to play fixed number of matches before eliminating or winning the tournament.
Each team has to play a match with each other teams exactly once then it is also a Round-Robin type of tournament.

• In a Round-Robin tournament, we will have a total nC2 matches.
For example, if there are 10 teams in a round-robin tournament and given that each team has to play with each other team exactly once then total number of matches (for a particular round) are nC2= 10C2= 45.

## Terms to remember

Seeds

seed is a competitor or a team in sports or other tournament who is given a preliminary ranking for the purposes of the draw. Players/teams are "planted" into the bracket in a manner that is typically intended so that the best do not meet until later in the competition.

RankPlayer NameCountry
1Andy MurrayGreat Britain
2Novak DjokovicSerbia
4Stan WawrinkaSwitzerland
5Kei NishikoriJapan
6Gael MonfilsFrance

If we take real life example, we can see that Andy Murray is the top ranked player, Novak Djokovic is the second ranked player, and so on.
So, in first round of a tournament, top ranked player is paired with last one, second ranked player is paired with second last one, till we reach to the middle two players.
Now, in second round, winner of the top most and winner of the bottom most are paired, and this process is continued till top 2 players can be paired for a match.

Upsets

An upset occurs in a competition, frequently in electoral politics or sports, when the party popularly expected to win (the favorite), is defeated by an underdog whom the majority expects to lose, defying the conventional wisdom. The underdog then becomes a giant-killer.
In 16 players tournament match fixtures will be like this.

In above diagram, we can see that 11 won against 6 in round of 16. So upset occurred at that point.

## Types of Questions

A) Knock-out tournament

In the table below is the listing of Teams, seeded from highest (#1) to lowest (#16), who are due to play in an Association of Cricket tournament. This tournament has three knockout rounds before the final, i.e., first round, Quarter-finals, and semi-finals. In the first round, the highest seeded team plays the lowest seeded team (seed#16) which is designated match No. 1 of first round; the 2nd seeded team plays with the 15th seeded team which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 8 of first round is to be played between 8th seeded team and the 9th seeded team. In the second round, the winner of match No. 1 of first round plays the winner of match No. 8 of first round and is designated match No. 1 of second round. Similarly, the winner of match No. 2 of first round plays the winner of match No. 7 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 4 of the second round is to be played between the winner of match No. 4 of first round and the winner of match No. 5 of first round. The same pattern is followed for later rounds as well.

Seed NumberTeam Name
1Australia
2India
3South-Africa
4Sri Lanka
5Pakistan
6England
7West Indies
8New Zealand
10Zimbabwe
11Kenya
12Netherlands
13Afghanistan
14UAE
15Bermuda
16Scotland

Questions

i) If there are no upsets in the first round, and only match Nos. 2, 3, and 4 of the second round result in upsets, then who would meet Pakistan in semi finals, in case Pakistan reaches semi finals?

a) India
b) England
c) Australia
d) Didn’t reach in semi finals

Solution:

In round 1 there were no upset, but in round two upsets in match No. 2, 3 and 4 (i.e. match between Seed No. 2 and 7, 3 and 6, 4 and 5 respectively).
So, Pakistan (i.e. Seed no. 5) will face Australia (i.e. Seed no. 1) in semi finals.

ii) If South-Africa and Sri-Lanka lose in the first round, while Bangladesh and India make it to the semifinals, then who would play with Australia in the second round, in the event Australia reaches second round?

b) Scotland
c) New Zealand
d) India

Solution:

According to given terms, Seed No. 2 (India) and 9 (Bangladesh) reaches semi-finals. So, they must have won all the preceding rounds.

So, from above diagram we can see that Bangladesh played against Australia in second round.

iii) If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then which team facing South-Africa in semi-finals?

a) Australia
b) West-Indies
c) Bermuda
d) India

Solution:

In the diagram, we can see that upsets are in even numbered matches i.e. matched between 2 and 15, 4 and 13, 6 and 11, 8 and 9 respectively.
And there are no upsets in second round.
So, from that in semi-finals South-Africa (Seed no. 3) faces West-Indies.

iv) How many matches are played in this tournament for getting final winner?

a) 32
b) 24
c) 16
d) 15

Solution:

In knockout tournament, total n - 1 matches are played for getting final winner. Here n=16, so total 16 - 1 = 15 matches are played.

B) Round-Robin Tournament

There are two key points for this type of question:

1. If we are finding maximum number or points for a team then start distribution of the point from bottom to top.
2. If we are finding minimum number or points for a team then start distribution of the point from top to bottom.

We will see above cases in following example.

Questions

There are 16 teams and they are divided into 2 groups of 8 each. Each team in a group plays against one another on a round-robin basis. Two points are awarded for a win, one point for a tie and zero for a loss. The top four teams from each group will qualify for the next round i.e. round 2. In Round 2, each team of one group will play with each team of group two. At the end of the second round, the top four teams in terms of the points scored advance to the semi finals and the winners of the semi finals play the finals. In case of teams having the same number of wins, the team with better run-rate would be ranked ahead.

(Note: Write down all the key points which are mentioned in the questions.
Like,
Total 16 teams
Two group - Each group having 8 teams.
Points - Win: 2, Tie / Draw: 1, Loss: 0
Top four from each group will go to the next round.(4 Matches)
Semi Finals (2 Matches), Final.)

Questions can be asked in this type of tournament based scenario:

i) What is the total number of matches played in the tournament?

a) 50
b) 56
c) 28
d) 75

Solution:

Total matches = Number of group A matches + Number of group B matches + Round 2 + Semi-Finals + Final
= 82 + 8C2 + 4C1 x 4C1 + 2 + 1
= 28 + 28 + 16 + 2 + 1 = 75 matches

ii) What is the least number of points with which a team can advance to the round 2?

a) 5
b) 4
c) 10
d) 8

Solution:

As we have seen in key points that if we are looking for minimum points then we will have to go from Top to Bottom.

In given question we have to find out "Least number of points" that means minimum number of points. SO we will have to start point distribution from Top to Bottom.

Now, let assume that top #1 team won all its 7 matches. (14 Points)
Top #2 team won all its matches except against #1 team. (12 Points)
Top #3 team won all its matches except against #1 and #2 matches. (10 Points)

Team numberPoints
114
212
310
4?
5?
6?
7?
8?

Now we are left with 20 points (i.e. Total points for group one matches 56 - (14 + 12 + 10) = 20).

Now remaining 5 teams have lost 3 matches with top teams. So, they are left with 4 matches with others. We will distribute remaining points equally to them i.e. 20 / 5 = 4.

So, remaining 5 teams will now have 4 - 4 points and here run rate checking scenario occurs.

Team numberPoints
114
212
310
44
54
64
74
84

So, minimum or least 4 Points are required for getting into second round.

iii) What is the maximum possible number of points that can be scored by a team that is eliminated at the firstround?

a) 14
b) 12
c) 10
d) 8

Solution:

In this case we have to find out maximum possible number of points that can be scored by a team which is eliminated after first round (Simply, by Low run rate)

As we have mentioned in key points that for finding maximum points we have to start from bottom to top.

We will make a group of Bottom 3 teams and another of Top 5 teams.

Let’s assume that bottom 3 team will lose their matches against top teams. So, they will have total 3 matches left for winning. (Those 3 teams will play against each other) Total 6 points they can have. We will distribute those points equally between them. i.e. 2 points for each team.

Team numberPoints
1?
2?
3?
4?
5?
62
72
82

Now, we have to give top 5 teams equal points. So that we can have top 4 team in next round and team #5 is eliminated after first round though it can have maximum number of points.

So, remaining 50 points (i.e. Total points 56 - 6 Points distributed amongst bottom 3 teams = 50 Points) will be distributed equally amongst 5 team that is 10.

Team numberPoints
110
210
310
410
510
62
72
82

Now, team #5 will also have 10 Points but it will be out of the league because of low run rate.

iv) What is the minimum number of matches won by a team that reaches the finals?

a) 1
b) 2
c) 3
d) 4

Solution:

This is very simple because we can assume that all the matches of every round before semi-finals are drawn, and team enters in semi-finals with high net run rate.
So, to reach in final, Team has to win only one match. i.e. Semi-Final.
(This is only possible when in the question "Draw/Tie" scenario is given.)

v) What is the maximum number of matches won by a team that reaches the finals?

a) 10
b) 16
c) 15
d) 12