Three children P, Q, R and two grown-ups X, Y play a badminton doubles tournament. X and Y are parents to two of the children playing. The child of X is not the same as the child of Y. Exactly one of the children does not have a parent playing in the tournament. The following rules are followed:
(i) A parent and his/her child cannot be on the same team.
(ii) A match can feature at most one parent and his/her child, that is, a maximum of one parent-child pair can play in a match.
The following matches were played:
TEAM 1 TEAM 2
MATCH 1 P and X Q and R
MATCH 2 P and R X and Y
MATCH 3 R and X Q and Y

Which one of the following options is correct?

Question

Three children P, Q, R and two grown-ups X, Y play a badminton doubles tournament. X and Y are parents to two of the children playing. The child of X is not the same as the child of Y. Exactly one of the children does not have a parent playing in the tournament. The following rules are followed:
(i) A parent and his/her child cannot be on the same team.
(ii) A match can feature at most one parent and his/her child, that is, a maximum of one parent-child pair can play in a match.
The following matches were played:

	TEAM 1	TEAM 2
MATCH 1	P and X	Q and R
MATCH 2	P and R	X and Y
MATCH 3	R and X	Q and Y

Which one of the following options is correct?

Prepp Team · Accepted Answer

Understanding the Badminton Tournament Setup

The puzzle involves five players: children P, Q, R and adults X, Y. We are given specific conditions:

X and Y are parents to two of the children (P, Q, R).
The child of X is different from the child of Y.
Exactly one child among P, Q, R does not have a parent playing in the tournament.
Rule (i): A parent and their child cannot be on the same team.
Rule (ii): A match can feature at most one parent-child pair (meaning a parent and their child cannot both be playing in the same match).

Deducing Parent-Child Relationships

We analyze the given matches using the rules:

Match 1 (P+X vs Q+R): Since X is paired with P, Rule (i) implies X cannot be P's parent.
Match 3 (R+X vs Q+Y): Since X is paired with R, Rule (i) implies X cannot be R's parent.
As X is a parent to one of the children (P, Q, R) and cannot be parent to P or R, it logically follows that X is the parent of Q.
Match 1 (P+X vs Q+R): Since Y is paired with R, Rule (i) implies Y cannot be R's parent.
Match 3 (R+X vs Q+Y): Since Y is paired with Q, Rule (i) implies Y cannot be Q's parent.
We know X is Parent(Q). Y is also a parent to one child. Since Y cannot be Parent(Q) or Parent(R), Y must be the parent of P.

Identifying the Unparented Child

From our deductions:

X is Parent(Q).
Y is Parent(P).
The condition states exactly one child does not have a parent playing. Since Q and P have playing parents (X and Y), R must be the child with no parent playing.

Verifying All Conditions

We confirm the deduced parentage (Parent(Q)=X, Parent(P)=Y, R is unparented) against the matches and rules:

Rule (i) Compliance: Q is not with X, and P is not with Y. This holds true based on the team assignments in the matches.
Rule (ii) Compliance: Check each match for featured parent-child pairs (parent and child both playing):
- Match 1 (P+X vs Q+R): Pair (X,Q) is featured (X & Q playing). Pair (Y,P) is not featured (Y not playing). Total = 1. Valid.
- Match 2 (P+R vs X+Y): Pair (X,Q) is not featured (Q not playing). Pair (Y,P) is featured (Y & P playing). Total = 1. Valid.
- Match 3 (R+X vs Q+Y): Pair (X,Q) is featured (X & Q playing). Pair (Y,P) is not featured (P not playing). Total = 1. Valid.
All conditions are met with R being the unparented child.