Question 1
Six persons Esha, Farhan, Bhanu, Deepak, Charu and Aman 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.
Charu sits second to the right of Aman. 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
- Charu second to the right of Aman:
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].
Charu = 2 CW from Aman: pos5 is 2 clockwise [solver-verified].
→ Aman at pos6, Charu 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:Charu → H3:Bhanu → H4:Farhan → H5:Deepak → H6:Aman
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
✓ Charu second to right of Aman
✓ 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
- Charu second to the right of Aman:
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].
Charu = 2 CW from Aman: pos5 is 2 clockwise [solver-verified].
→ Aman at pos6, Charu 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:Charu → H3:Bhanu → H4:Farhan → H5:Deepak → H6:Aman
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
✓ Charu second to right of Aman
✓ Deepak not adjacent to Esha
Answer: Deepak sits to the second to the right of Bhanu.