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