Among eight houses A, B, C, D, E, F, G and H, four houses are situated at the corners of a square - shaped garden. The remaining four houses are situated in the middle of each side of the square. All houses face the centre of the square. B is between A and H. F is to the immediate left of G. D is to immediate left of C, which is to the immediate left of F. B and F are in the middle of the two sides facing each other. D is not adjacent to H. Which four houses are situated at the corners.
A, C, G and H
- Corners: North-West (NW), North-East (NE), South-East (SE), South-West (SW)
- Middle of Sides: North (N), East (E), South (S), West (W)
- Clue 1: B is between A and H. Since A and H are corners, B must be the middle house situated between them. This implies A, B, H are in adjacent positions, e.g., A(NW), B(N), H(NE) or A(NE), B(E), H(SE) etc.
- Clue 2: B and F are in the middle of the two sides facing each other. If B is at the North (N) middle position, F must be at the South (S) middle position.
- Clue 3: D is not adjacent to H. H is a corner house. Its adjacent positions are the two middle points on the sides connected to it. Let's assume A is NW and H is NE (based on Clue 1 and B being N). H(NE) is adjacent to N middle (B) and E middle. Since D is a middle house, D cannot be N (occupied by B) or E middle. Therefore, D must be either S middle (occupied by F) or W middle. As D cannot be F, D must be the W middle position.
- Deduction of remaining middle house: With B at N, D at W, and F at S, the only remaining middle position is E at E middle.
- Current Arrangement Checkpoint:
- Corners: A, H, C, G
- Middles: B(N), D(W), F(S), E(E)
- Tentative Setup: A(NW), B(N), H(NE), E(E), {C/G}(SE), F(S), {G/C}(SW), D(W)
- Clue 4: F is to the immediate left of G. F is at the S middle position. If we assume 'left' means facing the center, the position immediately to the left of S middle is the SE corner. Therefore, G must be the SE corner.
- Clue 5: C is to the immediate left of F. C is a corner house, F is the S middle house. Facing the center from the S middle position, the immediate left is the SE corner. This implies C must also be the SE corner.
- Conflict Identification: Clues 4 and 5 both imply that the SE corner house is occupied by G and C, respectively. This indicates a potential contradiction or ambiguity in the problem statement's use of "left". However, since G must be a corner (based on the answer), and C must be a corner, and they are forced into the same position (SE) by the clues relative to F, let's re-evaluate.
- Revisiting Clues with Answer Constraint: We know the corners are A, C, G, H. Let's test the arrangement derived: A(NW), B(N), H(NE), E(E), C/G(SE), F(S), G/C(SW), D(W).
- B between A, H: A(NW)-B(N)-H(NE). Fits.
- B(N) and F(S) opposite middles: Fits.
- D not adjacent to H: H=NE. Adjacent N(B) & E(E). D=W. Fits.
- Check "F is to the immediate left of G": Assume G=SW corner. F=S middle. Facing S middle, left is SE corner. G is SW corner. This does NOT fit. Assume G=SE corner. F=S middle. Facing S middle, left is SE corner. This fits G=SE.
- Check "C is to the immediate left of F": Assume C=SE corner. F=S middle. Facing S middle, left is SE corner. This fits C=SE.
- Check "D is to the immediate left of C": Assume C=SE corner. Facing center from SE corner, left is SW corner. D should be SW corner. But D is a middle house (W middle). This does NOT fit.
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