1. Label the chairs 1 to 6 from left to right. 2. Clue 1: Priya (P) is at chair 1 or chair 6. 3. Clue 2: Rahul (R) is immediately to the right of Quentin (Q). This means they form a (Q R) block. 4. Clue 3: Tina (T) is exactly two chairs to the left of Sam (S). This forms a (T _ _ S) block. The possible chair pairs for (T,S) are (1,4), (2,5), (3,6). 5. Clue 4: Uma (U) is not next to Priya (P). 6. Clue 5: Rahul (R) is not next to Tina (T). Let's consider the two cases for Priya's position: Case 1: Priya (P) is in chair 1. Chairs: P _ _ _ _ _ (1 2 3 4 5 6) Now place the (T _ _ S) block. T cannot be in chair 1 as P is there. - If T is in chair 2, then S is in chair 5: P T _ _ S _ The remaining empty chairs are 3, 4, and 6. The (Q R) block must occupy chairs 3 and 4: P T Q R S _ The last person, Uma (U), must be in chair 6. This gives the arrangement: P T Q R S U (1 2 3 4 5 6). Check Clue 4: U (chair 6) is not next to P (chair 1). This is true. Check Clue 5: R (chair 4) is not next to T (chair 2). This is true. So, P T Q R S U is a valid arrangement. In this arrangement, Rahul (R) is in chair 4. - If T is in chair 3, then S is in chair 6: P _ T _ _ S The remaining empty chairs are 2, 4, and 5. The (Q R) block must occupy chairs 4 and 5: P _ T Q R S The last person, Uma (U), must be in chair 2. This gives the arrangement: P U T Q R S (1 2 3 4 5 6). Check Clue 4: U (chair 2) is next to P (chair 1). This contradicts Clue 4. So, this arrangement is invalid. Case 2: Priya (P) is in chair 6. Chairs: _ _ _ _ _ P (1 2 3 4 5 6) Now place the (T _ _ S) block. S cannot be in chair 6 as P is there. - If T is in chair 1, then S is in chair 4: T _ _ S _ P The remaining empty chairs are 2, 3, and 5. The (Q R) block must occupy chairs 2 and 3: T Q R S _ P The last person, Uma (U), must be in chair 5. This gives the arrangement: T Q R S U P (1 2 3 4 5 6). Check Clue 4: U (chair 5) is next to P (chair 6). This contradicts Clue 4. So, this arrangement is invalid. - If T is in chair 2, then S is in chair 5: _ T _ _ S P The remaining empty chairs are 1, 3, and 4. The (Q R) block must occupy chairs 3 and 4: _ T Q R S P The last person, Uma (U), must be in chair 1. This gives the arrangement: U T Q R S P (1 2 3 4 5 6). Check Clue 4: U (chair 1) is not next to P (chair 6). This is true. Check Clue 5: R (chair 4) is not next to T (chair 2). This is true. So, U T Q R S P is a valid arrangement. In this arrangement, Rahul (R) is in chair 4. In both valid arrangements (P T Q R S U and U T Q R S P), Rahul is consistently seated in chair 4. Why others are wrong:A — Quentin is in chair 3 in both valid arrangements. B — Tina is in chair 2 in both valid arrangements. D — Sam is in chair 5 in both valid arrangements.

Let the positions be P1, P2, P3, P4, P5 from left to right. 1. From Clue 3, BMW is at P2. So the arrangement starts as: __ BMW __ __ __ 2. From Clue 6, Honda is not at P1 or P5. Also, Honda is not Green. Since P2 is BMW, Honda must be at P3 or P4. 3. From Clue 2, the Volvo is immediately to the right of the Green car. Let's analyze the possible placements for the (Green, Volvo) pair: * It cannot be (P1, P2) because P2 is BMW, implying BMW is Volvo (contradiction). * It cannot be (P3, P4): If P3 is Green and P4 is Volvo. Since Honda is P3 or P4, Honda cannot be P3 (Green, Clue 6) or P4 (Volvo). So this is impossible. * It cannot be (P4, P5): If P4 is Green and P5 is Volvo. Honda (not P1, P5, or Green) must be P3. So we have: __ BMW Honda Green Volvo. The remaining cars are Audi and Ford, and positions P1 and P4 (which is Green). If Ford is P4, then Ford is Green, but Clue 4 says Ford is Black (contradiction). So P4 must be Audi (Green). This means P1 is Ford (Black). So: Ford(Black) BMW Honda Audi(Green) Volvo. Clue 1: Red car at P1 or P5. P1 is Black, so P5 (Volvo) must be Red. Clue 5: Audi (P4, Green) is next to White. The cars next to Audi are Honda (P3) and Volvo (P5, Red). So Honda (P3) must be White. This leaves BMW (P2) as Blue. But Clue 3 states BMW is not Blue (contradiction). 4. Therefore, the only remaining possibility for (Green, Volvo) is (P2, P3). * This means BMW is Green (P2) and Volvo is P3. * The row now is: __ BMW(Green) Volvo __ __ 5. From Clue 6, Honda is not P1 or P5, and not Green. Since BMW is Green (P2) and P3 is Volvo, Honda must be P4. * The row now is: __ BMW(Green) Volvo Honda __ 6. The remaining cars are Audi and Ford. The remaining positions are P1 and P5. 7. From Clue 1, the Red car is at P1 or P5. From Clue 4, Ford is Black and not next to the Red car. * If P1 is Audi and P5 is Ford: P1(Audi) P2(BMW,Green) P3(Volvo) P4(Honda) P5(Ford). Clue 4: Ford is Black, so P5 is Ford(Black). Clue 1: Red car at P1 or P5. Since P5 is Black, P1 must be Red. P1(Audi,Red). Now Clue 5: Audi is next to the White car. Audi is P1 (Red). The car next to it is P2 (BMW). So P2(BMW) must be White. But BMW is already Green (contradiction). * Therefore, P1 must be Ford and P5 must be Audi. * Row: Ford BMW(Green) Volvo Honda Audi 8. Now apply colors: * Clue 4: Ford is Black. So P1(Ford,Black). * Clue 1: Red car at P1 or P5. Since P1 is Black, P5 must be Red. So P5(Audi,Red). * Row with known colors: Ford(Black) BMW(Green) Volvo Honda Audi(Red) 9. Clue 5: The Audi is next to the White car. Audi is P5 (Red). The car next to it is P4 (Honda). So P4(Honda) must be White. * Row with known colors: Ford(Black) BMW(Green) Volvo Honda(White) Audi(Red) 10. The remaining car for a color is Volvo (P3). The remaining color is Blue. So P3(Volvo,Blue). * Final deduced arrangement: P1: Ford (Black), P2: BMW (Green), P3: Volvo (Blue), P4: Honda (White), P5: Audi (Red). 11. Let's verify this against all clues: * 1. Red car at one end (Audi is Red at P5). YES. * 2. Volvo right of Green (BMW is Green at P2, Volvo at P3). YES. * 3. BMW is P2 (YES) and not Blue (BMW is Green). YES. * 4. Ford is Black (Ford at P1 is Black, YES) and not next to Red (Ford P1 not next to Audi P5). YES. * 5. Audi is next to White (Audi P5 next to Honda P4, and Honda is White). YES. * 6. Honda not Green (Honda P4, Green is BMW P2. YES) and not at an end (Honda P4). YES. All clues are satisfied. The car in the third position from the left (P3) is the Volvo. Why others are wrong:A — Audi is at position 5. B — BMW is at position 2. C — Honda is at position 4.

Let the positions in the queue be P1, P2, P3, P4, P5 from front to back. 1. From Clue 1, Amy (A) is in the exact middle, so A = P3. The queue is (_ _ A _ _). 2. From Clue 5, David (D) is not immediately next to Amy (P3). This means D cannot be P2 or P4. Therefore, D must be P1 or P5. 3. From Clue 3, Emma (E) is not at either end. So E cannot be P1 or P5. This means E must be P2 or P4. 4. From Clue 2, Ben (B) and Chloe (C) are a block (BC), with B immediately in front of C. Since A is P3, the BC block cannot be (P2, P3) or (P3, P4). Thus, the BC block must be (P1, P2) or (P4, P5). 5. From Clue 4, David (D) is in front of Ben (B), meaning D's position number is less than B's position number. Let's test the possibilities for David's position: Scenario 1: D = P1. The queue starts with (D _ A _ _). Remaining people: B, C, E. Remaining spots: P2, P4, P5. Place E (must be P2 or P4 from step 3): Subcase 1.1: E = P2. Queue: (D E A _ _). Remaining people: B, C. Remaining spots: P4, P5. Place the (B,C) block (from step 4). The only possible consecutive spots are (P4, P5). So, B = P4 and C = P5. The full queue is (D1 E2 A3 B4 C5). Let's check all clues: - Clue 1 (Amy is P3): Valid. - Clue 2 (Chloe (C5) is immediately behind Ben (B4)): Valid. - Clue 3 (Emma (E2) is not P1 or P5): Valid. - Clue 4 (David (D1) is in front of Ben (B4)): Valid (1 < 4). - Clue 5 (David (D1) is not immediately next to Amy (A3)): Valid (E2 is between them). This solution is consistent with all clues. Subcase 1.2: E = P4. Queue: (D _ A E _). Remaining people: B, C. Remaining spots: P2, P5. There are no two consecutive spots available for the (B,C) block. So this subcase is invalid. Scenario 2: D = P5. The queue ends with (_ _ A _ D). Remaining people: B, C, E. Remaining spots: P1, P2, P4. Place E (must be P2 or P4 from step 3): Subcase 2.1: E = P2. Queue: (_ E A _ D). Remaining people: B, C. Remaining spots: P1, P4. There are no two consecutive spots available for the (B,C) block. So this subcase is invalid. Subcase 2.2: E = P4. Queue: (_ _ A E D). Remaining people: B, C. Remaining spots: P1, P2. Place the (B,C) block (from step 4). The only possible consecutive spots are (P1, P2). So, B = P1 and C = P2. The full queue is (B1 C2 A3 E4 D5). Let's check all clues: - Clue 1 (Amy is P3): Valid. - Clue 2 (Chloe (C2) is immediately behind Ben (B1)): Valid. - Clue 3 (Emma (E4) is not P1 or P5): Valid. - Clue 4 (David (D5) is in front of Ben (B1)): INVALID (5 is not less than 1). This solution is inconsistent with Clue 4. Therefore, the only valid arrangement is (D1 E2 A3 B4 C5). Second from the front (P2) is Emma. Why others are wrong:A — Amy is in the third position (P3). B — Ben is in the fourth position (P4). C — Chloe is in the fifth position (P5).

Let's denote the five positions from left to right as 1, 2, 3, 4, 5. Clue 1 states R is exactly in the middle, so R is at position 3. ( _ _ R _ _ ) Clue 3 states P is not at either end (1 or 5), so P must be at position 2 or 4. Clue 2 states Q is immediately to the right of T, meaning T and Q are adjacent in that order (TQ). Clue 4 states there are exactly two houses between S and Q (S _ _ Q). Let's consider the two possibilities for P: Case 1: P is at position 2. The arrangement starts as ( _ P R _ _ ). From S _ _ Q, if Q were at position 4, then S would be at position 1 (S P R Q _). The remaining house is T, which would be at position 5. So the arrangement becomes S P R Q T. Now let's check Clue 2: Q is immediately to the right of T. In S P R Q T, Q is at position 4 and T is at position 5. Q is to the left of T, which contradicts Clue 2. Therefore, P cannot be at position 2. Case 2: P is at position 4. The arrangement starts as ( _ _ R P _ ). From S _ _ Q, Q cannot be at position 1 (as S would need to be at position -2, which is impossible). If Q is at position 2, then S must be at position 5 (S is 5, with R and P between Q at 2). So the arrangement is ( _ Q R P S ). The remaining position is 1, and the remaining house is T. So T is at position 1. The complete arrangement is T Q R P S. Let's verify this arrangement (T Q R P S) with all clues: 1. House R is exactly in the middle. (R is at position 3) - Consistent. 2. House Q is immediately to the right of House T. (T is at position 1, Q is at position 2) - Consistent. 3. House P is not at either end. (P is at position 4) - Consistent. 4. There are exactly two houses between House S and House Q. (S is at position 5, Q is at position 2, with R and P in between them) - Consistent. All clues are satisfied by the arrangement T Q R P S. The house at the far left end of the street (position 1) is T. Why others are wrong:A — P is at position 4. B — Q is at position 2. C — R is at position 3.

Let the positions in the queue be numbered 1, 2, 3, 4, 5 from front to back. From the clue "Carol is exactly in the middle of the queue", Carol is in position 3. Current queue: [_, _, Carol, _, _] From the clue "Bob is immediately behind David", David and Bob must be in consecutive positions (D, B). Possible (D, B) pairs are (1,2) or (4,5), as position 3 is occupied by Carol. Assume (D, B) is (1,2): Queue: [David, Bob, Carol, _, _] The remaining people are Alice and Emily. The remaining positions are 4 and 5. From the clue "Alice is not at either end of the queue", Alice cannot be in position 5 (an end). So Alice must be in position 4. This places Emily in position 5. Proposed queue: [David, Bob, Carol, Alice, Emily] Now check the remaining clue: "Emily is ahead of David". In this arrangement, Emily is in position 5 and David is in position 1. Emily is not ahead of David. This contradicts the clue. Therefore, the assumption (D, B) is (1,2) is incorrect. Assume (D, B) is (4,5): Queue: [_, _, Carol, David, Bob] The remaining people are Alice and Emily. The remaining positions are 1 and 2. From the clue "Alice is not at either end of the queue", Alice cannot be in position 1 (an end). So Alice must be in position 2. This places Emily in position 1. Proposed queue: [Emily, Alice, Carol, David, Bob] Let's check all clues with this arrangement: 1. Alice is not at either end (Alice is 2nd). True. 2. Bob is immediately behind David (David 4th, Bob 5th). True. 3. Carol is exactly in the middle (Carol 3rd). True. 4. Emily is ahead of David (Emily 1st, David 4th). True. All clues are satisfied. The queue order is Emily (1st), Alice (2nd), Carol (3rd), David (4th), Bob (5th). Therefore, Alice is second in the queue. Why others are wrong:B — David is fourth in the queue. C — Emily is first in the queue. D — Bob is fifth in the queue.