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