Solving the Six Friends Linear Arrangement Puzzle

This question requires us to determine the seating arrangement of six friends sitting in a straight line based on the given clues. Let's break down the information and build the arrangement step by step.

Analyzing the Clues and Building the Arrangement

We are given the following clues:

• Six friends are sitting in a straight line.
• E is 4th from the right.
• E is between B and D.
• A is adjacent to B.
• D is adjacent to C.
• D is between E and C.
• F is adjacent to C.

Let's use the most definite clue first:

Clue 1: E is 4th from the right.

Since there are six positions in the line, let's number them from left to right:

Position 1 - Position 2 - Position 3 - Position 4 - Position 5 - Position 6

If E is 4th from the right, counting from the right end (Position 6), E will be at Position 3.

Arrangement so far: \_\_\_ \_\_\_ E \_\_\_ \_\_\_ \_\_\_

(Position 1 - Position 2 - Position 3 - Position 4 - Position 5 - Position 6)

Clue 2: D is between E and C.

This tells us that D is immediately next to both E and C. The sequence must be E-D-C or C-D-E. Since E is at Position 3, and D is next to E, D must be at Position 2 or Position 4. If D is at Position 2, C would be at Position 1 (C-D-E). If D is at Position 4, C would be at Position 5 (E-D-C).

Clue 3: E is between B and D.

This tells us that E is immediately next to both B and D. The sequence must be B-E-D or D-E-B. Since E is at Position 3, and D is next to E, D must be at Position 2 or Position 4. We already established this with Clue 2.

Let's combine Clue 2 and Clue 3. Both clues state relationships involving E and D. Clue 2: D is between E and C $\implies$ E-D-C or C-D-E. Clue 3: E is between B and D $\implies$ B-E-D or D-E-B.

Considering E is at Position 3:

• If the sequence is D-E-B (from Clue 3), then D is at Position 2 and B is at Position 4. Arrangement: \_\_\_ D E B \_\_\_ \_\_\_ \_\_\_
• If the sequence is B-E-D (from Clue 3), then B is at Position 2 and D is at Position 4. Arrangement: \_\_\_ B E D \_\_\_ \_\_\_ \_\_\_

Now let's use Clue 2 again: D is between E and C (E-D-C or C-D-E).

• Option 1 (from Clue 3): D is at Position 2, E is at Position 3, B is at Position 4. The sequence around E is D-E-B. For D to be between E and C (Clue 2), C must be at Position 1 (C-D-E). Arrangement: C D E B \_\_\_ \_\_\_ Let's check if E is between B and D in this arrangement: C (D) E (B). E is between D and B. This fits.
• Option 2 (from Clue 3): B is at Position 2, E is at Position 3, D is at Position 4. The sequence around E is B-E-D. For D to be between E and C (Clue 2), C must be at Position 5 (E-D-C). Arrangement: \_\_\_ B E D C \_\_\_ Let's check if E is between B and D in this arrangement: \_\_\_ (B) E (D) C \_\_\_. E is between B and D. This fits.

We have two potential partial arrangements:

1. C D E B \_\_\_ \_\_\_
2. \_\_\_ B E D C \_\_\_

Clue 4: A is adjacent to B.

• For arrangement 1 (C D E B \_\_\_ \_\_\_), B is at Position 4. The adjacent positions are 3 (E) and 5. Since A must be adjacent to B and cannot be E, A must be at Position 5. Arrangement: C D E B A \_\_\_
• For arrangement 2 (\_\_\_ B E D C \_\_\_), B is at Position 2. The adjacent positions are 1 and 3 (E). Since A must be adjacent to B and cannot be E, A must be at Position 1. Arrangement: A B E D C \_\_\_

We now have two potential arrangements with only one spot left:

1. C D E B A \_\_\_
2. A B E D C \_\_\_

Clue 5: F is adjacent to C.

• For arrangement 1 (C D E B A \_\_\_), C is at Position 1. The only adjacent position is 2 (D). F cannot be adjacent to C here as D is already there. This arrangement is incorrect.
• For arrangement 2 (A B E D C \_\_\_), C is at Position 5. The adjacent positions are 4 (D) and 6. Since F must be adjacent to C and cannot be D, F must be at Position 6. Arrangement: A B E D C F

The final arrangement is A B E D C F.

Verifying the Final Arrangement

Let's check if this arrangement satisfies all clues:

• Six friends in a line: A, B, E, D, C, F. Yes.
• E is 4th from the right: Counting from F (right end), F is 1st, C is 2nd, D is 3rd, E is 4th. Yes.
• E is between B and D: The sequence is B-E-D. Yes.
• A is adjacent to B: A is next to B. Yes.
• D is adjacent to C: D is next to C. Yes.
• D is between E and C: The sequence is E-D-C. Yes.
• F is adjacent to C: F is next to C. Yes.

All clues are satisfied by the arrangement: A B E D C F.

Identifying Who is Between F and D

The final arrangement is A B E D C F. We need to find who is sitting between F and D. Looking at the arrangement:

A B E D C F

The person sitting between D and F is C.

Therefore, C is sitting between F and D.

Conclusion

Based on the step-by-step analysis of the clues, the final arrangement of the six friends is A B E D C F. In this arrangement, C is located between F and D.

Revision Table: Key Seating Arrangement Clues

Additional Information on Linear Arrangement Puzzles

Linear arrangement puzzles are a common type of logical reasoning question found in competitive exams. They require you to arrange individuals or objects in a straight line based on a set of clues that specify their relative positions.

Key strategies for solving linear arrangement puzzles:

• Start with clues that provide absolute positions (like "X is 3rd from the left" or "Y is at an end").
• Identify clues that define relationships between two or three individuals (like "A is next to B" or "C is between D and E").
• Combine clues to build partial arrangements.
• Look for clues that help eliminate possibilities or connect different parts of the arrangement.
• Use diagrams or draw lines to represent the positions and fill in the names as you deduce them.
• Always verify your final arrangement against all the given clues to ensure accuracy.
• Pay close attention to terms like "adjacent" (immediately next to) and "between" (immediately between unless specified otherwise, and typically involving exactly three people in that specific sequence).

Practicing different types of linear arrangement problems helps improve speed and accuracy in competitive settings.