# CRE 2 - Knockout Tournament | DI - Games & Tournaments

**Answer the next 10 questions based on the information given below:**

64 players taking part in a knockout tennis tournament are seeded from 1 to 64 with seed 1 being the top seed, seed 2 the second seed and so on. In the first round, seed 1 plays seed 64 which is termed match 1 of round 1, seed 2 plays seed 63 which is termed match 2 of round 1 and so on till match 32 of round 1 where seed 32 plays seed 33.

In the next round, the winner of match 1 of round 1 plays the winner of the last match (match 32) of round 1, the winner of match 2 of round 1 plays the winner of the second last match (match 31) of round 1 and so on. This continues till only one player is left undefeated.

If in any match a lower seeded player defeats a higher seeded player, it is called an upset.

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

What is the total number of rounds in the tournament?

Answer: 6

**Explanation** :

As there are a total of 64 players, in the first round 32 players would be eliminated and 32 players will advance to the 2nd round.

In the 2^{nd} round half of 32, i.e., 16 players would be eliminated and 16 will advance to 3^{rd} round.

Similarly,

In 3^{rd} round ⇒ 8 will be eliminated and 8 will advance to 4th round.

In 4^{th} round (QF) ⇒ 4 will be eliminated and 4 will advance to 5th round.

In 5^{th} round (SF) ⇒ 2 will be eliminated and 2 will advance to 6th round.

In 6^{th} round (Final) ⇒ This is final round and winner of the tournament will be decided in this round.

**Alternately,**

If the number of players in a knock-out tournament is 2^{k}, then the number of rounds is k.

Here, number of players is 64 = 2^{6}, hence number of rounds is 6.

Hence, 6.

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

How many matches are played in the tournament?

- A.
52

- B.
60

- C.
63

- D.
64

Answer: Option C

**Explanation** :

Consider the solution for the first question of this set.

Total number of matches = 32 + 16 + 8 + 4 +2 + 1 = 63.

**Alternately,**

As the tournament stated with 64 players and in the end only one player was the champion, rest 63 players are eliminated each in 1 match. To eliminate 63 players, we need to play 63 matches.

Hence, option (c).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

If the tournament had no upsets, in which round was the player seeded 13 eliminated?

- A.
2

- B.
3

- C.
4

- D.
5

Answer: Option B

**Explanation** :

In case of no upsets

**Round 1**: Top 32 players will win their respective matches. Player seeded 13 will also win its match and advance to round 2.

**Round 2**: Top 16 players will win their respective matches. Player seeded 13 will also win its match and advance to round 3.

**Round 3**: Top 8 players will win their respective matches. Player seeded 13 will not be able to win its match and hence gets knocked out in round 3.

∴ The player seeded 13 was eliminated in the 3^{rd} round.

Hence, option (b).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

How many matches did the player who lost in the semi-finals, win in the tournament?

- A.
2

- B.
3

- C.
4

- D.
5

Answer: Option C

**Explanation** :

As the player reached the semi-finals, he was among the last 4 players i.e., he reached till round 5.

∴ He must have his matches in each of the previous 4 rounds and reached the 5^{th} round.

⇒ The player reaching semi-finals would have won 4 matches and lost in semi-finals.

Hence, option (c).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

Which player faced the player seeded 5 in the quarter finals (round of 8) if the tournament had no upsets?

- A.
6

- B.
9

- C.
11

- D.
4

Answer: Option D

**Explanation** :

In any round, in case of no upsets, the sum of the seedings of the players is one more than the number of players left in the tournament.

As the match happens in the quarterfinals, the number of players left = 8.

∴ Sum of seedings of players = 8 + 1 = 9.

Since 9 – 5 = 4, player seeded 5 faced the player seeded 4 in the quarterfinals.

**Alternately,**

For n^{th} seeded player:

⇒ match no. played by n^{th} seeded player in a round = n^{th} ; if n ≤ total no. of matches in that round.

⇒ match no. played by n^{th} seeded player in a round = (sum of the seeds – n)^{th} match if n > total no. of matches in that round.

For e.g., 4^{th} seeded player will play 5^{th} match till round 3.

In 4^{th} round 5^{th} seeded player will play 9 – 5 = 4^{th} match.

Hence, we can draw the following table:

Both 5^{th} and 4^{th} seeded players play the 4^{th} match of Round 4.

Hence, option (d).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

If each player is involved in at most one upset, then who could be the lowest seeded player winning the tournament?

- A.
47

- B.
33

- C.
31

- D.
32

- E.
None of these

Answer: Option B

**Explanation** :

Given: A player can be involved in at most one upset.

If all the players are involved in upsets in the 1^{st} round itself, then players seeded 33 till 64 will advance to the 2^{nd} round.

From second round onwards there can not be any upsets hence highest seeded player i.e., player seeded 33 will win the tournament.

Hence, option (b).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

If there are only 5 upsets in the tournament, then who could be the lowest seeded player winning the tournament?

- A.
16

- B.
17

- C.
63

- D.
32

- E.
None of these

Answer: Option D

**Explanation** :

We can use options to solve this question.

**Option (c):** For player seeded 63, he will have to do 6 upsets (1 in each of the 6 rounds) to win the tournament. Hence, with 5 upsets he cannot win the tournament.

**Option (d)**: Player seeded 32 will win its match in round 1 without upset (he will play against player seeded 33).

From round 2^{nd} onwards if he is involved in 1 upset for every round, he can win the tournament with 5 upsets.

Hence, the lowest seeded player that can win the tournament with 5 upsets is player seeded 32.

Hence, option (d).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

If upsets are allowed, which of the following seeded player could have faced the player seeded 14 in the second round?

- A.
48

- B.
46

- C.
47

- D.
49

Answer: Option B

**Explanation** :

For n^{th} seeded player:

⇒ match no. played by n^{th} seeded player in a round = nth match; if n ≤ total no. of matches in that round.

⇒ match no. played by n^{th} seeded player in a round = (sum of the seeds – n)^{th} match; if n > total no. of matches in that round.

For e.g., 14^{th} seeded player will play 14^{th} match in round 2.

Now 46^{th} player will play 19^{th} match in round 1. If this match results in an upset i.e., 46^{th} seeded player wins he will advance to 2^{nd} round and play the match which 19^{th} seeded player was supposed to play.

Now 19^{th} seeded player would have played 33 – 19 = 14^{th} match in 2^{nd} round.

Since both 46^{th} and 14^{th} seeded players play the same match (14^{th} match) of round 2,

⇒ 46^{th} seeded player plays against 14^{th} seeded player in round 2.

We can draw the following table:

Hence, option (d).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

If the player seeded 46 won the tournament, then which of the players cannot be the runner- up?

- A.
36

- B.
43

- C.
45

- D.
44

- E.
Can't be determined

Answer: Option B

**Explanation** :

A player cannot be the runner-up if he plays seed 43 before the final round.

From the table we can see that seed 43 plays its round 4 match against seed 46. Since seed 46 will win this match, seed 43 cannot reach final and hence cannot be the runner-up.

Hence, option (b).

Workspace:

**CRE 2 - Knockout Tournament | DI - Games & Tournaments**

If one of the matches was between the players seeded 37 and 43, then another match in the same tournament can be between players seeded

- A.
9 & 13

- B.
36 & 48

- C.
15 & 51

- D.
10 & 23

- E.
More than one of the above

Answer: Option D

**Explanation** :

Let us figure out the match no. played by each of these players in each of the rounds.

Since upsets are allowed, a lower seeded player can also advance to next rounds.

Assuming, m > n,

In a round if a match is between seed m and seed n there is upset, seed m advances to next round.

In next round seed m will play the match which seed n was supposed to play.

Two players will have played against each other if they play the same match of a particular round.

Hence, we can draw the following table for the match number played by each of the players.

From the table we can see that seed 37 and seed 43 will play each other in the Final match of the tournament.

**Option (a)**: Seed 9 and Seed 13 do not play any match amongst themselves till round 4, after which seed 13 will be eliminated by seed 43. They will not be able to play against each other in further rounds.

**Option (b)**: Seed 36 and Seed 48 do not play any match amongst themselves till round 4, after which seed 36 will be eliminated by seed 37. They will not be able to play against each other in further rounds.

**Option (c)**: Seed 15 and Seed 51 do not play any match amongst themselves till round 4, after which seed 51 will be eliminated by seed 43. They will not be able to play against each other in further rounds.

**Option (d)**: Seed 10 and seed 23 play against each other in 2^{nd} round before they get eliminated.

Hence, seed 10 and 23 play against each other.

Hence, option (d).

Workspace:

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