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