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