Question 1
Eight persons D, B, A, G, C, E, H and F are sitting around a square table.
Four persons sit at corners and four at the middle of sides, all facing the center.
D sits at a corner. B sits second to the right of D.
A sits at the middle of a side and is not adjacent to D.
G sits opposite to D. C sits at a corner immediately to the right of A.
E sits immediately to the left of B. H is not adjacent to G.
How many persons sit between D and G when counted from the left of D?
Solution Approach:
Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) → M1(2) → C2(3) → M2(4) → C3(5) → M3(6) → C4(7) → M4(8) → back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7
Step 2: Place persons systematically
- D sits at a corner → pos 1
- B sits second to the RIGHT of D: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- G sits OPPOSITE D (pos 1) → pos 5 ✓
- A at midpoint, NOT adjacent to D(pos 1):
Adjacent to pos 1: pos 8 and pos 2
A → pos 6 (midpoint, not adjacent) ✓
- C sits at corner immediately to the RIGHT of A(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓
Step 3: Remaining persons
Remaining: E, H, F
Fill remaining seats: pos2=E, pos8=H, pos4=F
Final Arrangement (clockwise):
pos1:D → pos2:E → pos3:B → pos4:F → pos5:G → pos6:A → pos7:C → pos8:H
Step 4: Count from LEFT of D to G
Left = anti-clockwise direction from D(pos 1):
pos1(D) → pos8(H) → pos7(C) → pos6(A) → pos5(G)
Persons between (excluding D and G): pos8(H), pos7(C), pos6(A)
Count = 3 person(s)
Answer: Three person(s) sit between D and G.
Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) → M1(2) → C2(3) → M2(4) → C3(5) → M3(6) → C4(7) → M4(8) → back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7
Step 2: Place persons systematically
- D sits at a corner → pos 1
- B sits second to the RIGHT of D: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- G sits OPPOSITE D (pos 1) → pos 5 ✓
- A at midpoint, NOT adjacent to D(pos 1):
Adjacent to pos 1: pos 8 and pos 2
A → pos 6 (midpoint, not adjacent) ✓
- C sits at corner immediately to the RIGHT of A(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓
Step 3: Remaining persons
Remaining: E, H, F
Fill remaining seats: pos2=E, pos8=H, pos4=F
Final Arrangement (clockwise):
pos1:D → pos2:E → pos3:B → pos4:F → pos5:G → pos6:A → pos7:C → pos8:H
Step 4: Count from LEFT of D to G
Left = anti-clockwise direction from D(pos 1):
pos1(D) → pos8(H) → pos7(C) → pos6(A) → pos5(G)
Persons between (excluding D and G): pos8(H), pos7(C), pos6(A)
Count = 3 person(s)
Answer: Three person(s) sit between D and G.