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