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