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