Only two people sit between D and G. Only E sits to the right of K. Only one person sits between G and K. C sits at some place to the right of B but at some place to the left of F.
Who sits third from the right end of the line?
Solving the Seating Arrangement Puzzle
This puzzle involves arranging seven people (B, C, D, E, F, G, K) in a straight line facing north based on several conditions. The goal is to determine who is seated third from the right end.
Key Constraints Explained
Let's break down the information given:
- There are 7 people: B, C, D, E, F, G, K.
- They sit in a straight line facing North. We can represent the positions from left to right as 1, 2, 3, 4, 5, 6, 7.
- Constraint 1: Only two people sit between D and G. (D _ _ G or G _ _ D)
- Constraint 2: Only E sits to the right of K. This implies K and E are adjacent, with K immediately to the left of E (KE).
- Constraint 3: Only one person sits between G and K. (G _ K or K _ G)
- Constraint 4: C sits to the right of B, and C sits to the left of F. (B ... C ... F)
Step-by-Step Deduction
Combining Constraints on K, E, and G
From Constraint 2, we know the block KE must exist. Now consider Constraint 3 (G _ K or K _ G):
- Case 1: If G _ K, combined with KE, it forms the block G _ KE. This block uses 4 people.
- Case 2: If K _ G, combined with KE, it forms the block KE _ G. This block also uses 4 people.
Incorporating Constraint 1 (D and G)
Now let's integrate Constraint 1 (D _ _ G or G _ _ D) with the blocks derived above.
- Analyzing Case 1 (G _ KE):
- If D _ _ G: Combining with G _ KE, we need two people between D and G. This suggests an arrangement like D _ _ G _ KE. This sequence uses 7 positions: D, X, Y, G, Z, K, E.
- If G _ _ D: This doesn't fit easily with the G _ KE block without violating the spacing.
- Analyzing Case 2 (KE _ G):
- If D _ _ G: Placing this relative to KE _ G could lead to arrangements like D _ KE _ G or D _ _ KE _ G. Checking spacing: D _ KE _ G uses 6 people and implies 3 people (K, E, _) between D and G, contradicting Constraint 1. A structure like D X Y KE Z G uses 7 people and satisfies D _ _ G (DXYG) and K _ G (KEZG). It also satisfies Constraint 2 (KE).
- If G _ _ D: Combining with KE _ G gives KE _ G _ _ D. This uses 7 positions and satisfies Constraint 1 (G _ _ D), Constraint 2 (KE), and Constraint 3 (K _ G).
Applying Constraint 4 (B, C, F) and Finalizing
Now we place B, C, F according to B ... C ... F into the potential structures.
- Evaluating Case 1 structure: D _ _ G _ KE The empty slots are positions 2, 3, and 5. The people to place are B, C, F. We need B ... C ... F. The only way to fit B, C, F into the slots (2, 3, 5) respecting the order is: B in 2, C in 3, F in 5. This gives the final arrangement: D B C G F K E. Let's verify all constraints for D B C G F K E: 1. D _ _ G: D B C G (2 people between D and G) - ✓ OK. 2. KE: K E (E is immediately right of K) - ✓ OK. 3. G _ K: G F K (1 person 'F' between G and K) - ✓ OK. 4. B ... C ... F: B C F (C is right of B, C is left of F) - ✓ OK. This arrangement is valid.
- Evaluating Case 2 structure: KE _ G _ _ D The empty slots are positions 3, 6, and 7. The people to place are B, C, F. We need B ... C ... F. Trying to place them leads to arrangements like K E B G C F D. Checking constraints for K E B G C F D: 1. G _ _ D: G C F D (C, F between G and D) - ✓ OK. 2. KE: K E - ✓ OK. 3. K _ G: K E B G (E, B between K and G) - X Fails! Constraint 3 says *only one* person between K and G. This arrangement has two. Therefore, this structure derived from Case 2 is invalid.
- Evaluating Case 2 structure: D X Y KE Z G The empty slots are X, Y, Z. People B, C, F need to be placed. We need B ... C ... F. A possible placement is D B C KE F G. Checking constraints for D B C KE F G: 1. D _ _ G: D B C G (B, C between D and G) - ✓ OK. 2. KE: K E - ✓ OK. 3. K _ G: K E F G (E, F between K and G) - X Fails! Constraint 3 requires only one person between K and G. This structure is also invalid.
Final Arrangement and Answer
The only valid arrangement satisfying all conditions is:
| Position (Left to Right) | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| People | D | B | C | G | F | K | E |
Now, let's find the person third from the right end:
- The person at the right end (7th position) is E.
- The person second from the right end (6th position) is K.
- The person third from the right end (5th position) is F.
Therefore, F sits third from the right end of the line.
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Important Questions from Seating arrangement
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(i) C is seated next to A
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1. D is seated next to B
2. E is seated next to A
3. D and C are separated by two seats
Select the correct answer using the code given below:
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