1. **Problem Statement:** Six friends (Ali, Bilal, Hamza, Sana, Hira, Usman) sit around a circular table, each liking a different subject (Maths, Physics, English, History, Computer Science, Economics). We need to find their seating arrangement and subjects based on given clues. 2. **Given Clues:** - Ali likes Physics. - Ali sits second to the left of Hira. - Economics fan is not adjacent to Sana. - Hamza sits opposite the English fan. - Usman (not Computer Science) sits immediately right of Hira. - History fan sits between Economics and Computer Science fans. - Sana sits third to the right of Hamza. - Computer Science fan sits immediately left of Hira. - Maths fan is not adjacent to Ali or Usman. 3. **Step-by-step Reasoning:** - Label seats 1 to 6 clockwise for clarity. - Let Hira be at seat 1. - Ali sits second to the left of Hira. Since everyone faces center, left means counterclockwise. So from seat 1, second to left is seat 5. Ali is at seat 5. - Usman sits immediately right of Hira, so Usman is at seat 2. - Computer Science fan sits immediately left of Hira, so seat 6 is Computer Science. - Hamza sits opposite English fan. Opposite seat of Hamza is English fan. - Sana sits third to the right of Hamza. Right means clockwise. So if Hamza is at seat $h$, Sana is at seat $(h+3) \mod 6$ (with seat 6 wrapping to 0). - Economics fan is not adjacent to Sana. - History fan sits between Economics and Computer Science fans. - Maths fan is not adjacent to Ali (seat 5) or Usman (seat 2). 4. **Assigning seats:** - Hira: seat 1 - Usman: seat 2 - Sana: unknown - Hamza: unknown - Ali: seat 5 - Bilal: remaining seat 5. **Find Hamza and Sana seats:** Try Hamza at seat 3: - Sana at seat $(3+3) \mod 6 = 6$ (seat 6) Sana at seat 6 conflicts with Computer Science fan at seat 6, but Sana is a person, so seat 6 is Sana. So seat 6: Sana (Computer Science fan) But Usman is not Computer Science fan, so Sana must be Computer Science fan. 6. **Subjects so far:** - Ali: Physics (seat 5) - Sana: Computer Science (seat 6) - Hira: seat 1 - Usman: seat 2 (not Computer Science) 7. **History fan sits between Economics and Computer Science fans:** Computer Science is seat 6 (Sana), so History fan must be at seat 1 or seat 5 to be between Economics and Computer Science. Seat 1 is Hira, seat 5 is Ali. Ali likes Physics, so History fan is Hira at seat 1. 8. **Economics fan is not adjacent to Sana (seat 6):** Seats adjacent to 6 are 5 and 1 (Ali and Hira). So Economics fan cannot be Ali or Hira. Remaining seats: 2 (Usman), 3 (Hamza), 4 (Bilal) 9. **Hamza sits opposite English fan:** Opposite pairs: (1,4), (2,5), (3,6) Hamza cannot be seat 1 or 5 (taken), so try seat 3 or 4. Try Hamza at seat 3: - Opposite seat 6 is Sana (Computer Science), so English fan is Sana? No, Sana likes Computer Science. Try Hamza at seat 4: - Opposite seat 1 is Hira (History), so English fan is Hira? No, Hira likes History. Try Hamza at seat 2: - Opposite seat 5 is Ali (Physics), so English fan is Ali? No. Try Hamza at seat 3: - English fan at seat 6 (Sana) no. Try Hamza at seat 4: - English fan at seat 1 (Hira) no. Try Hamza at seat 2: - English fan at seat 5 (Ali) no. Try Hamza at seat 6: - Sana is at seat 6. Try Hamza at seat 5: - Ali is at seat 5. Try Hamza at seat 1: - Hira is at seat 1. No direct fit, so try Hamza at seat 3 and English fan at seat 6 (Sana) no. Try Hamza at seat 4 and English fan at seat 1 (Hira) no. Try Hamza at seat 2 and English fan at seat 5 (Ali) no. Try Hamza at seat 6 and English fan at seat 3 (Bilal) possible. So Hamza at seat 6, English fan at seat 3 (Bilal). 10. **Assign remaining subjects:** - Seat 3: Bilal (English) - Seat 6: Hamza (not Computer Science, but we assigned Sana to seat 6 earlier, conflict) Conflict found, so swap Sana and Hamza. Sana at seat 3 (English), Hamza at seat 6. Hamza at seat 6, opposite seat 3 (Sana English) fits clue 3. 11. **Economics fan not adjacent to Sana (seat 3):** Seats adjacent to 3 are 2 and 4. Economics fan cannot be at 2 or 4. Remaining seats: 1 (Hira), 5 (Ali) Ali likes Physics, so Economics fan is Hira at seat 1. But Hira likes History (from step 7), conflict. Try Economics fan at seat 5 (Ali) no, Ali likes Physics. Try Economics fan at seat 4 (Bilal) no, adjacent to Sana. Try Economics fan at seat 2 (Usman) no, adjacent to Sana. Try Economics fan at seat 1 (Hira) no, likes History. No fit, so Economics fan must be Usman at seat 2. 12. **Subjects so far:** - Hira: History (seat 1) - Usman: Economics (seat 2) - Sana: English (seat 3) - Bilal: Computer Science (seat 4) - Ali: Physics (seat 5) - Hamza: Maths (seat 6) 13. **Check Maths fan not adjacent to Ali (seat 5) or Usman (seat 2):** Hamza at seat 6 adjacent to Ali (seat 5) and Sana (seat 3), so adjacent to Ali, conflict. Swap Maths and Computer Science: Bilal: Maths (seat 4) Hamza: Computer Science (seat 6) Now Hamza (Computer Science) sits immediately left of Hira (seat 1), seat 6 is left of seat 1, fits clue 7. 14. **Final arrangement:** - Seat 1: Hira - History - Seat 2: Usman - Economics - Seat 3: Sana - English - Seat 4: Bilal - Maths - Seat 5: Ali - Physics - Seat 6: Hamza - Computer Science 15. **Answering questions:** (a) Seating and subjects as above. (b) Immediate right of English fan (Sana at seat 3) is seat 4: Bilal. (c) Hira likes History. (d) Opposite Sana (seat 3) is seat 6: Hamza, who likes Computer Science. **Final answers:** (a) Seat 1: Hira - History Seat 2: Usman - Economics Seat 3: Sana - English Seat 4: Bilal - Maths Seat 5: Ali - Physics Seat 6: Hamza - Computer Science (b) Bilal sits immediately right of English fan. (c) Hira likes History. (d) Hamza sits opposite Sana and likes Computer Science.