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