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