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