Question 1
Six persons Charu, Bhanu, Farhan, Aman, Esha and Deepak are sitting around a hexagonal table, one at each corner, all facing the center.
Charu sits opposite to Bhanu. Farhan sits second to the right of Charu.
Esha sits second to the right of Deepak. Aman is not adjacent to Charu.
What is the position of Aman with respect to Farhan?
Solution Approach:
Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.
Step 2: Place definite positions
- Fix Charu at H1 (pos 1).
- Charu opposite Bhanu: opp(pos1) = pos4 → Bhanu at H4
Step 3: Apply relative positioning
- Farhan second to the right of Charu(pos1):
CW 2: pos1→pos2→pos3
→ Farhan at H3
- Esha second to the right of Deepak:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Charu=1, Bhanu=4, Farhan=3,
remaining seats: [2, 5, 6].
Esha = 2 CW from Deepak: pos5 is 2 clockwise [solver-verified].
→ Deepak at pos6, Esha at pos2
Step 4: Apply constraint
- Aman not adjacent to Charu(pos1):
Adjacent to pos1: pos6 and pos2
→ Aman at pos5 (not adjacent) ✓
Final Arrangement (clockwise):
H1:Charu → H2:Esha → H3:Farhan → H4:Bhanu → H5:Aman → H6:Deepak
Step 5: Find Aman's position relative to Farhan
Farhan at pos3, Aman at pos5.
pos5 is 2 clockwise from pos3.
Verification:
✓ Charu opposite Bhanu
✓ Farhan second to right of Charu
✓ Esha second to right of Deepak
✓ Aman not adjacent to Charu
Answer: Aman sits to the second to the right of Farhan.
Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.
Step 2: Place definite positions
- Fix Charu at H1 (pos 1).
- Charu opposite Bhanu: opp(pos1) = pos4 → Bhanu at H4
Step 3: Apply relative positioning
- Farhan second to the right of Charu(pos1):
CW 2: pos1→pos2→pos3
→ Farhan at H3
- Esha second to the right of Deepak:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Charu=1, Bhanu=4, Farhan=3,
remaining seats: [2, 5, 6].
Esha = 2 CW from Deepak: pos5 is 2 clockwise [solver-verified].
→ Deepak at pos6, Esha at pos2
Step 4: Apply constraint
- Aman not adjacent to Charu(pos1):
Adjacent to pos1: pos6 and pos2
→ Aman at pos5 (not adjacent) ✓
Final Arrangement (clockwise):
H1:Charu → H2:Esha → H3:Farhan → H4:Bhanu → H5:Aman → H6:Deepak
Step 5: Find Aman's position relative to Farhan
Farhan at pos3, Aman at pos5.
pos5 is 2 clockwise from pos3.
Verification:
✓ Charu opposite Bhanu
✓ Farhan second to right of Charu
✓ Esha second to right of Deepak
✓ Aman not adjacent to Charu
Answer: Aman sits to the second to the right of Farhan.