Among sevens friends A, B, C, D, E, F and G, G is elder than A and C. C is elder than D. F is elder than one friend only. A is third eldest. E is the youngest. G is younger than B. Who is the eldest?
B
Age Ordering Puzzle Solution
This question is a logic puzzle that requires us to determine the relative ages of seven friends: A, B, C, D, E, F, and G. We are given several clues about their ages, and our goal is to find out who among them is the eldest.
Analyzing the Clues
Let's list down the given clues:
- G is elder than A and C.
- C is elder than D.
- F is elder than one friend only.
- A is third eldest.
- E is the youngest.
- G is younger than B.
Step-by-Step Deduction to Determine Age Order
We can determine the age order from eldest to youngest based on the clues. There are 7 friends, so we can think of 7 positions from 1st (eldest) to 7th (youngest).
- The clue "E is the youngest" tells us that E is in the 7th position. Order: _ _ _ _ _ _ E
- The clue "F is elder than one friend only" means F is older than exactly one person. Since E is the youngest, F must be older than only E. This places F in the 6th position (second youngest). Order: _ _ _ _ _ F E
- The clue "A is third eldest" places A in the 3rd position. Order: _ _ A _ _ F E
- The clue "G is elder than A and C". Since A is in the 3rd position, G must be elder than A. This means G must be in position 1 or 2.
- The clue "G is younger than B" means B is elder than G. Since G must be in position 1 or 2, B must be elder than G. If G were in position 1, no one could be elder than G, which contradicts $G < B$. Therefore, G cannot be in position 1.
- Combining the deductions from steps 4 and 5, G must be in the 2nd position. Order: _ G A _ _ F E
- Now we have B, C, and D remaining to fill positions 1, 4, and 5.
- The clue "G is elder than C" tells us C is younger than G. Since G is in position 2, C cannot be in position 1. C must be in position 4 or 5.
- The clue "C is elder than D" tells us C is older than D. If C were in position 5, D would have to be younger than C. However, positions 6 and 7 are already filled by F and E, so D cannot be placed younger than C if C is in position 5. Therefore, C must be in position 4. Order: _ G A C _ F E
- Since C is in position 4 and is elder than D, D must be in position 5. Order: _ G A C D F E
- The only remaining friend is B, and the only remaining position is the 1st position. So, B must be the eldest. Order: B G A C D F E
Final Age Ranking
Based on the step-by-step deduction, the friends are ranked by age from eldest to youngest:
B > G > A > C > D > F > E
Identifying the Eldest Friend
The eldest friend is the one in the first position of the ranking.
From the final ranking B > G > A > C > D > F > E, the friend in the first position is B.
Therefore, B is the eldest.
Revision Table: Summary of Age Relations
| Friend | Relative Age Clues | Deduced Position (1st=Eldest, 7th=Youngest) |
| E | Youngest | 7th |
| F | Elder than one friend only (E) | 6th |
| A | Third eldest | 3rd |
| G | Elder than A & C, Younger than B | 2nd |
| C | Elder than D, Younger than G | 4th |
| D | Younger than C | 5th |
| B | Elder than G | 1st |
Additional Information: Logical Reasoning Puzzles
This problem is a classic example of a logical reasoning puzzle involving relative ordering. To solve such puzzles effectively, follow these tips:
- Read all clues carefully before starting.
- Identify absolute positions first (like youngest, eldest, or a specific numbered position).
- Use relative clues to narrow down possible positions for others.
- Draw diagrams or lists to keep track of possibilities and eliminate options.
- Verify your final arrangement against all the original clues to ensure consistency.
Practicing different types of ordering and ranking puzzles helps improve logical deduction skills.
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