This article will be about a famous category of questions that more often than not appears in LR section of CAT. Games and Tournaments involves data based on some tournament in some set format like your IPL,Premier League or your US open. We are supposed to resolve certain conflicts and reach answers regarding various scenarios that might come up during that tournament. Today, we look at this LR set from CAT 2005 and try to develop the acumen for solving such problems on a more generic scale with time.
Q. In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed #32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No. 16 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. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.
Q1) If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?
(1) Justine Henin (2) Nadia Petrova (3) Patty Schnyder (4) Venus Williams
Q2) If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?
(1) Dinara Safina (2) Justine Henin (3) Nadia Petrova (4) Patty Schnyder
Q3) 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 who could be the lowest seeded player
facing Maria Sharapova in semi-finals?
(1) Anastasia Myskina (2) Flavia Pennetta (3) Nadia Petrova (4) Svetlana Kuznetsova
Q4) If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?
(1) Amelie Mauresmo (2) Elena Dementieva (3) Kim Clijsters (4) Lindsay Davenport
In such questions you choose your template for gathering information in an organized manner. Being aware of the sport does help at times but is not a mandatory requirement. Choosing a structure such as following is ideal for this problem or any problem that involves draws being made and tournament being run in rounds.
Round 1
M1 : 1,32
M2 : 2,31
M3 : 3,30
..
M8 : 8,25
M9 : 9,24
M10: 10,23
..
M15: 15,18
M16: 16,17
Round 2
MM1 : M1,M16
MM2 : M2,M15
MM3 : M3,M14
MM4 : M4,M13
MM5 : M5,M12
MM6 : M6,M11
MM7 : M7,M10
MM8 : M8,M9
Quarters
Q1 : MM1,MM8
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5
Semis
S1 : Q1,Q4
S2 : Q2,Q3
Finals
F : S1,S2
Question1 :
Davenport
Track her seed position.Seed 2
Round 1 : Beats 31
Round 2 : Beats 15
Quarters : Faces winner of MM7 : Upset.So M10 -> Seed 10
Answer : Venus Williams(Option 4)
Question 2 :
In front of your template,keep adding what's given
6,8 lose in second round.
7,9 reach semis
Track Sharapova : 1
Round 1
M1 : 1,32 : 1
M2 : 2,31
M3 : 3,30
..
M6 : 6,27 : 6
M7 : 7,26 : 7
M8 : 8,25 : 8
M9 : 9,24 : 9
M10: 10,23
..
M15: 15,18
M16: 16,17
Round 2
MM1 : M1,M16 : 1
MM2 : M2,M15
MM3 : M3,M14
MM4 : M4,M13
MM5 : M5,M12
MM6 : M6,M11 : 11
MM7 : M7,M10 : 7
MM8 : M8,M9 : 9
Quarters
Q1 : MM1,MM8 : 9 -> Petrova. Petrova wins
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5
Semis
S1 : Q1,Q4
S2 : Q2,Q3
Answer : Petrova(Option 3)
Question 3 :
Round 1
M1 : 1,32
M2 : 2,31 : 31
M3 : 3,30
..
M8 : 8,25 : 25
M9 : 9,24
M10: 10,23 : 23
..
M15: 15,18
M16: 16,17 : 17
Round 2
MM1 : M1,M16 : 1
MM2 : M2,M15 : 31,15 : 15
MM3 : M3,M14 : 3
MM4 : M4,M13 : 29,13 : 13
MM5 : M5,M12 : 5
MM6 : M6,M11 : 27,11 : 11
MM7 : M7,M10 : 7
MM8 : M8,M9 : 25,9 : 9
Quarters
Q1 : MM1,MM8 : 1(Sharapova reaches semis)
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5 : 13,5 : For lowest seed in semis for Sharapova, we take the upset.
Seed 13 wins.
Semis
S1 : Q1,Q4 : Sharapova Vs Seed 13(Anastasia Myskina)
S2 : Q2,Q3
Answer : Anastasia Myskina(Option 1)
Question 4 :
Since question is for who wouldn't face. We write losers this time
Round 1
M1 : 1,32 : 32
M2 : 2,31 : 31
M3 : 3,30 : 30
..
M8 : 8,25 : 25
M9 : 9,24
M10: 10,23
..
M15: 15,18
M16: 16,17
Round 2
MM1 : M1,M16 : 16
MM2 : M2,M15 : 15
MM3 : M3,M14 : 14
MM4 : M4,M13 : 13
MM5 : M5,M12 : 12
MM6 : M6,M11 : 11
MM7 : M7,M10 : 10
MM8 : M8,M9 : 9
Quarters
Q1 : MM1,MM8 : 8
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5
Semis
S1 : Q1,Q4 : 4
S2 : Q2,Q3
Finals
F : S1,S2
Options :
Seed 3,6,4,2
Obviously the answer is option 3. Seed 4 must lose in semis for Sharapova to be in the final.
Key Notes :
1) Choosing the right template is very important. Choose a table,structure of format that will allow you to run the question for multiple iterations. Like here you could simply write seed numbers for each question one after the other for each question. Solutions looks long but with the right template you would hardly have taken 6-7 minutes for all the questions.
2) Make key observations : Seed 1 plays Seed 32 , Seed 2 plays Seed 31 : 1 + 32 = 2 + 31 = 33
Same for round 2 : M1 plays M16, M2 plays M15 : 1 + 16 = 2 + 15 = 17
Will allow you to process faster.
3) Number of matches played in such an arrangement : 16 + 8 + 4 + 2 + 1 = 31 = 32 - 1. Always.
Check how much you learned by solving a similar problem uploaded in the practice arena. Leave comments there for your answer. Will share approach in case of doubts or queries.
In the next article we'll take up another kind of games and tournament problem where in a tabular wins,losses,draws is involved.
Cheers!
AS
Q. In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed #32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16th seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of first round plays the winner of match No. 16 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. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.
Q1) If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?
(1) Justine Henin (2) Nadia Petrova (3) Patty Schnyder (4) Venus Williams
Q2) If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semi-finals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?
(1) Dinara Safina (2) Justine Henin (3) Nadia Petrova (4) Patty Schnyder
Q3) 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 who could be the lowest seeded player
facing Maria Sharapova in semi-finals?
(1) Anastasia Myskina (2) Flavia Pennetta (3) Nadia Petrova (4) Svetlana Kuznetsova
Q4) If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?
(1) Amelie Mauresmo (2) Elena Dementieva (3) Kim Clijsters (4) Lindsay Davenport
In such questions you choose your template for gathering information in an organized manner. Being aware of the sport does help at times but is not a mandatory requirement. Choosing a structure such as following is ideal for this problem or any problem that involves draws being made and tournament being run in rounds.
Round 1
M1 : 1,32
M2 : 2,31
M3 : 3,30
..
M8 : 8,25
M9 : 9,24
M10: 10,23
..
M15: 15,18
M16: 16,17
Round 2
MM1 : M1,M16
MM2 : M2,M15
MM3 : M3,M14
MM4 : M4,M13
MM5 : M5,M12
MM6 : M6,M11
MM7 : M7,M10
MM8 : M8,M9
Quarters
Q1 : MM1,MM8
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5
Semis
S1 : Q1,Q4
S2 : Q2,Q3
Finals
F : S1,S2
Question1 :
Davenport
Track her seed position.Seed 2
Round 1 : Beats 31
Round 2 : Beats 15
Quarters : Faces winner of MM7 : Upset.So M10 -> Seed 10
Answer : Venus Williams(Option 4)
Question 2 :
In front of your template,keep adding what's given
6,8 lose in second round.
7,9 reach semis
Track Sharapova : 1
Round 1
M1 : 1,32 : 1
M2 : 2,31
M3 : 3,30
..
M6 : 6,27 : 6
M7 : 7,26 : 7
M8 : 8,25 : 8
M9 : 9,24 : 9
M10: 10,23
..
M15: 15,18
M16: 16,17
Round 2
MM1 : M1,M16 : 1
MM2 : M2,M15
MM3 : M3,M14
MM4 : M4,M13
MM5 : M5,M12
MM6 : M6,M11 : 11
MM7 : M7,M10 : 7
MM8 : M8,M9 : 9
Quarters
Q1 : MM1,MM8 : 9 -> Petrova. Petrova wins
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5
Semis
S1 : Q1,Q4
S2 : Q2,Q3
Answer : Petrova(Option 3)
Question 3 :
Round 1
M1 : 1,32
M2 : 2,31 : 31
M3 : 3,30
..
M8 : 8,25 : 25
M9 : 9,24
M10: 10,23 : 23
..
M15: 15,18
M16: 16,17 : 17
Round 2
MM1 : M1,M16 : 1
MM2 : M2,M15 : 31,15 : 15
MM3 : M3,M14 : 3
MM4 : M4,M13 : 29,13 : 13
MM5 : M5,M12 : 5
MM6 : M6,M11 : 27,11 : 11
MM7 : M7,M10 : 7
MM8 : M8,M9 : 25,9 : 9
Quarters
Q1 : MM1,MM8 : 1(Sharapova reaches semis)
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5 : 13,5 : For lowest seed in semis for Sharapova, we take the upset.
Seed 13 wins.
Semis
S1 : Q1,Q4 : Sharapova Vs Seed 13(Anastasia Myskina)
S2 : Q2,Q3
Answer : Anastasia Myskina(Option 1)
Question 4 :
Since question is for who wouldn't face. We write losers this time
Round 1
M1 : 1,32 : 32
M2 : 2,31 : 31
M3 : 3,30 : 30
..
M8 : 8,25 : 25
M9 : 9,24
M10: 10,23
..
M15: 15,18
M16: 16,17
Round 2
MM1 : M1,M16 : 16
MM2 : M2,M15 : 15
MM3 : M3,M14 : 14
MM4 : M4,M13 : 13
MM5 : M5,M12 : 12
MM6 : M6,M11 : 11
MM7 : M7,M10 : 10
MM8 : M8,M9 : 9
Quarters
Q1 : MM1,MM8 : 8
Q2 : MM2,MM7
Q3 : MM3,MM6
Q4 : MM4,MM5
Semis
S1 : Q1,Q4 : 4
S2 : Q2,Q3
Finals
F : S1,S2
Options :
Seed 3,6,4,2
Obviously the answer is option 3. Seed 4 must lose in semis for Sharapova to be in the final.
Key Notes :
1) Choosing the right template is very important. Choose a table,structure of format that will allow you to run the question for multiple iterations. Like here you could simply write seed numbers for each question one after the other for each question. Solutions looks long but with the right template you would hardly have taken 6-7 minutes for all the questions.
2) Make key observations : Seed 1 plays Seed 32 , Seed 2 plays Seed 31 : 1 + 32 = 2 + 31 = 33
Same for round 2 : M1 plays M16, M2 plays M15 : 1 + 16 = 2 + 15 = 17
Will allow you to process faster.
3) Number of matches played in such an arrangement : 16 + 8 + 4 + 2 + 1 = 31 = 32 - 1. Always.
Check how much you learned by solving a similar problem uploaded in the practice arena. Leave comments there for your answer. Will share approach in case of doubts or queries.
In the next article we'll take up another kind of games and tournament problem where in a tabular wins,losses,draws is involved.
Cheers!
AS
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