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