Difficulty: Medium
Correct Answer: Grandmother
Explanation:
Introduction / Context:
This is a seating and positioning puzzle phrased as a family photograph situation. You are given relative positions of five family members: father, son, grandmother, mother and daughter. The question asks who is in the middle of the group when they are arranged in a line. Understanding left and right relations and combining them into a single order are the main skills tested.
Given Data / Assumptions:
- The father stands to the right of the son.
- The father stands to the left of the grandmother.
- The mother sits to the left of her daughter.
- The mother sits to the right of the grandmother.
- All five persons are in one row for the photograph.
Concept / Approach:
The approach is to translate each sentence into a left–right ordering constraint. Once you know who must be left or right of whom, you can merge the constraints into a single linear arrangement. The person who ends up with exactly two people on each side (in a five-person arrangement) is the one in the middle. No arithmetic is needed, only careful reading and placement.
Step-by-Step Solution:
Step 1: From the father is standing to the right of the son and to the left of the grandmother, we get this partial order (from left to right): Son – Father – Grandmother.
Step 2: From the mother is sitting to the left of her daughter, we know Mother must be somewhere to the left of Daughter in the final lineup.
Step 3: From the mother is sitting to the right of the grandmother, we get Grandmother – Mother – Daughter in left–right order.
Step 4: Combine both partial orders. We already have Son – Father – Grandmother from Step 1 and Grandmother – Mother – Daughter from Step 3. Merging them yields: Son – Father – Grandmother – Mother – Daughter.
Step 5: Count positions from left to right. There are five people, so the third position is the exact middle of the group. In the order Son – Father – Grandmother – Mother – Daughter, the third person is Grandmother.
Verification / Alternative check:
Check that all original conditions are satisfied by the final order Son – Father – Grandmother – Mother – Daughter. The father is indeed to the right of the son and to the left of the grandmother. The mother is to the right of the grandmother and to the left of the daughter. Every constraint matches perfectly. Since no alternative arrangement can satisfy all the given left–right relations simultaneously, this order is unique, and the person in the third position is definitely the grandmother.
Why Other Options Are Wrong:
- Son: He is at the extreme left with four people to his right, not in the middle.
- Father: He is second from the left, with one person on his left and three on his right.
- Mother: She is fourth from the left, with three people on her left and one on her right.
- Daughter: She is at the extreme right with four people on her left.
Common Pitfalls:
One common mistake is to misread to the right of as immediately to the right of. The statements only specify relative positions, not adjacency, so you must keep the order flexible until all constraints are combined. Another pitfall is to forget to include all five family members in the final sequence, which can lead to a wrong middle person. Drawing a simple line and placing names step by step can greatly reduce confusion.
Final Answer:
The person positioned in the middle of the group is the grandmother.
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