# PE 1 - Puzzles | LR - Puzzles

**Answer the next 3 questions based on the information given below.**

Mr. and Mrs. Sharma and Mr. and Mrs. Oberoi are playing a chess tournament. They play a total of 3 games. Following information is know

- No person won more than one match.
- The Sharmas won more games than the Oberois.
- The men won two games and the women won one game.
- Only in the first game were two players married to each other.
- Anyone who lost a game cannot play the very next game and
- The person who won a game definitely played the next game.

**PE 1 - Puzzles | LR - Puzzles**

Who did not play a game?

- A.
Mrs. Sharma

- B.
Mr. Oberoi

- C.
Mrs. Oberoi

- D.
Mr. Sharma

Answer: Option C

**Explanation** :

Sharma win more matches than Oberois, i.e., Sharmas should win at least 2 out of 3 matches.

**Case 1:** Considering Sharmas play the first match.

Case 1(i): Mr. Sharma wins the match

If Mr. Sharma wins the 1st match he can’t win the 2nd match. (A person cannot win more than 1 match)

Mrs. Sharma will have to play the 3rd match and win it since Sharmas have to win at least 2 matches.

Since men have to win 2 matches, Mr. Oberoi will have to win the 2nd match.

Case 1(ii): Mrs. Sharma wins the match

If Mrs. Sharma wins the 1st match she can’t win the 2nd match. (A person cannot win more than 1 match)

Mr. Sharma will have to play the 3rd match and win it since Sharmas have to win at least 2 matches.

Since men have to win 2 matches, Mr. Oberoi will have to win the 2nd match.

**Case 2**: Considering Oberois play the first match.

Case 2 (i): Mr. Oberoi wins the match

If Mr. Oberoi wins the 1st match he can’t win the 2nd match.

Sharma have to win the remaining 2 games.

Since men have to win 2 matches, Mr. Oberoi will have to win the 2nd match.

This is not possible since in only the first match a couple played.

Case 2(ii): Mrs. Oberoi wins the match

If Mrs. Oberoi wins the first match, Sharmas will have to win the next two matches.

But men have to win 2 matches hence Mr. Sharma will have to win the remaining matches which is not possible since a person cannot win more than one match.

∴ This can is also not possible.

∴ Only two cases are possible:

**Final Case 1: **

**Final Case 2: **

Hence, option (c).

Workspace:

**PE 1 - Puzzles | LR - Puzzles**

Who won the second match?

- A.
Mr. Sharma

- B.
Mr. Oberoi

- C.
Mrs. Sharma

- D.
Mrs. Oberoi

Answer: Option B

**Explanation** :

Consider the solution to the first question of this set.

Mr. Oberoi won the second match

Hence, option (b).

Workspace:

**PE 1 - Puzzles | LR - Puzzles**

How many games did Mr. Oberoi win?

Answer: 1

**Explanation** :

Consider the solution to the first question of this set.

Mr. Oberoi won exactly 1 match.

Hence, option 1.

Workspace:

**Answer the next 4 questions based on the information given below.**

6 players – P, Q, R, S, T and U - are divided equally into two teams X and Y. They are playing a game comprising of three rounds. In every round each player tosses a coin exactly once.

For every player of team X if Heads comes up the player gets Rs. 100 whereas if Tails comes up the player gets only Rs. 50.

For every player of team Y if Tails comes up the player gets Rs. 100 whereas if Heads comes up the player gets only Rs. 50.

The following table gives the information regarding total money won by each of the 6 players till Round 1, 2 and 3.

It is also known that Heads comes up 2, 3 and 4 times in round 1, 2 and 3 respectively.

**PE 1 - Puzzles | LR - Puzzles**

The teams of how many players can be uniquely determined?

Answer: 2

**Explanation** :

We are given the cumulative amount received by each of the players till round 1, 2 and 3.

∴ We can calculate the amount each of them receives in each round.

**Round 1**: We know heads turns up exactly 2 times.

There can be three cases for this.

Case 1: Heads turns up for 2 players from team X.

Case 2: Heads turns up for 1 player each from both teams.

Case 3: Heads turns up for 2 players from team Y.

Since 3 players receive Rs. 100 and 3 other players receive Rs. 50 in round 1 hence, only case 2 is possible.

∴ 3 players receiving Rs. 100 are P, R and S. One of them is from team X and other 2 from team Y …**(1)**

**Round 2:** We know heads turns up exactly 3 times.

There can be three cases for this.

Case 1: Tails turns up for 3 players from team X.

Case 2: Tails turns up for 2 players from X and 1 player from Y.

Case 3: Tails turns up for 1 player from X and 2 players from Y.

Case 4: Tails turns up for 3 players from team Y.

Since 4 players receive Rs. 100 and 2 other players receive Rs. 50 in round 2 hence, only case 2 is possible.

∴ 4 players receiving Rs. 100 are Q, S, T and U and

2 players receiving Rs. 50 are P and R. One of them is from team X and other from team Y …**(2)**

**Round 3:** We know heads turns up exactly 4 times.

There can be three cases for this.

Case 1: Tails turns up for 2 players from team X.

Case 2: Tails turns up for 1 player each from both teams.

Case 3: Tails turns up for 2 players from team Y.

Since 3 players receive Rs. 100 and 3 other players receive Rs. 50 in round 3 hence, only case 2 is possible.

∴ 3 players receiving Rs. 100 are P, R and T. One of them is from team Y and other 2 from team X …**(3)**

From (1): One of P, R and S is from team X and other 2 from team Y.

From (2): One of P and R is from team X and other from team Y.

From (3): One of P, R and T is from team Y and other 2 from team X.

(1) & (2) ⇒ S is from team Y

(3) & (2) ⇒ T is from team X

(1), (2) & (3) ⇒ One of Q and U is from team X and other from team Y.

Hence, 2.

**Video Solution**:

Workspace:

**PE 1 - Puzzles | LR - Puzzles**

Which of the following pairs definitely has one player from both teams?

- A.
P and R

- B.
S and P

- C.
P and Q

- D.
None of these

Answer: Option A

**Explanation** :

Consider the solution to first question of this set.

One of P and R is from team X and other from team Y.

Hence, option (a).

**Video Solution**:

Workspace:

**PE 1 - Puzzles | LR - Puzzles**

Out of the times when all the three players from team X threw a die, how many times did heads turn up?

Answer: 5

**Explanation** :

Consider the solution to first question of this set.

From round 1, one player from team X got heads.

From round 2, two players from team X got heads.

From round 3, two players from team X got heads.

∴ Team X got heads 4 times

Hence, 5.

Workspace:

**PE 1 - Puzzles | LR - Puzzles**

How much money (in Rs.) did the players from team Y receive in all the three rounds?

Answer: 700

**Explanation** :

Consider the solution to first question of this set.

S is from team Y and S received Rs. 250.

One of P and R is from team Y and each of them receives Rs. 250.

One of Q and U is from team Y and each of them receives Rs. 200.

∴ Total amount received by players from team Y is 250 + 250 + 200 = Rs. 700.

Hence, option (a).

**Video Solution**:

Workspace:

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