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