Question 1
Six family members — Varun (grandfather), Sita (grandmother), Rohan (father), Heena (mother), Rajesh (son), and Pooja (daughter) — are sitting around a circular table facing the center.
No male sits adjacent to another male. Heena sits second to the right of Sita.
Rohan is not adjacent to his wife. Rajesh is not adjacent to Sita.
Who sits immediately to the right of Pooja?
Solution Approach:
Step 1: Identify genders
Males: Varun, Rohan, Rajesh
Females: Sita, Heena, Pooja
Step 2: Apply no-adjacent-males constraint
With 3 males and 3 females in a circle of 6, "no two males adjacent" forces strict alternation:
M, F, M, F, M, F (clockwise)
Step 3: Build the arrangement
Position 1: a Male. Let Varun at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.
Step 4: Apply the mother-grandmother constraint
Heena sits second to the RIGHT of Sita (right=CW):
Female positions: 2, 4, 6.
- If Sita=pos2 → Heena=pos4 ✓ (or pos2+2=pos4)
- If Sita=pos4 → Heena=pos6 ✓
- If Sita=pos6 → Heena=pos8%6=pos2 ✓
Step 5: Apply father-not-adjacent-to-mother (wife) constraint
Rohan's wife = Heena.
Rohan not adjacent to Heena.
Male positions: 1, 3, 5. Female positions: 2, 4, 6.
Testing Sita=pos4 → Heena=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father ≠ pos5 and ≠ pos1 → Rohan=pos3 ✓.
Remaining males: Varun(1), Rajesh(5). Pooja and Sita fill pos2, pos4.
Sita=pos4 (as set). Pooja=pos2 ✓.
Final Arrangement:
pos1:Varun → pos2:Heena → pos3:Rajesh → pos4:Pooja → pos5:Rohan → pos6:Sita
Verification:
✓ No adjacent males: Varun(1)-Pooja(2), Rohan(3)-Sita(4), Rajesh(5)-Heena(6) — all M-F pairs
✓ Heena(pos6) second right of Sita(pos4): CW 2 from pos4 = pos6 ✓
✓ Rohan(pos3) not adjacent to Heena(pos6): pos3 and pos6 are not adjacent ✓
Find immediately to the right of Pooja:
Pooja at pos 4. Right (CW) = pos 5 = Rohan.
Answer: Rohan sits immediately to the right of Pooja.
Step 1: Identify genders
Males: Varun, Rohan, Rajesh
Females: Sita, Heena, Pooja
Step 2: Apply no-adjacent-males constraint
With 3 males and 3 females in a circle of 6, "no two males adjacent" forces strict alternation:
M, F, M, F, M, F (clockwise)
Step 3: Build the arrangement
Position 1: a Male. Let Varun at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.
Step 4: Apply the mother-grandmother constraint
Heena sits second to the RIGHT of Sita (right=CW):
Female positions: 2, 4, 6.
- If Sita=pos2 → Heena=pos4 ✓ (or pos2+2=pos4)
- If Sita=pos4 → Heena=pos6 ✓
- If Sita=pos6 → Heena=pos8%6=pos2 ✓
Step 5: Apply father-not-adjacent-to-mother (wife) constraint
Rohan's wife = Heena.
Rohan not adjacent to Heena.
Male positions: 1, 3, 5. Female positions: 2, 4, 6.
Testing Sita=pos4 → Heena=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father ≠ pos5 and ≠ pos1 → Rohan=pos3 ✓.
Remaining males: Varun(1), Rajesh(5). Pooja and Sita fill pos2, pos4.
Sita=pos4 (as set). Pooja=pos2 ✓.
Final Arrangement:
pos1:Varun → pos2:Heena → pos3:Rajesh → pos4:Pooja → pos5:Rohan → pos6:Sita
Verification:
✓ No adjacent males: Varun(1)-Pooja(2), Rohan(3)-Sita(4), Rajesh(5)-Heena(6) — all M-F pairs
✓ Heena(pos6) second right of Sita(pos4): CW 2 from pos4 = pos6 ✓
✓ Rohan(pos3) not adjacent to Heena(pos6): pos3 and pos6 are not adjacent ✓
Find immediately to the right of Pooja:
Pooja at pos 4. Right (CW) = pos 5 = Rohan.
Answer: Rohan sits immediately to the right of Pooja.