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