Image X represents the six faces of a cube. Image Y shows a composition using five such cubes. What could be the rear view of the shown composition?
Show Hint
If you encounter a spatial reasoning problem that seems to have contradictory information, double-check your initial analysis (like face pairings). If the contradiction persists, the question may be flawed. In a test, you might have to guess or look for a non-obvious pattern.
Step 1: Understanding the Concept:
This is a spatial reasoning puzzle involving the unfolding (net) of a cube and an assembly made of these cubes. We need to deduce the appearance of the hidden faces to construct the rear view. A crucial first step is to determine the arrangement of faces on the cube, specifically which faces are opposite each other.
Step 2: Key Formula or Approach:
1. Analyze the net (Image X) to find the pairs of opposite faces. Imagine folding the net into a cube.
2. For each cube in the assembly (Image Y), use the known visible faces and the opposite-face rule to deduce the hidden faces, particularly the rear face.
3. Combine the rear faces of all five cubes in their correct positions to form the rear view.
Step 3: Detailed Explanation: 1. Analyzing the Net (Image X):
If we take the central column (2-4-1-3) and fold it, with 4 as the base, then 2 and 1 become opposite side walls, and 5 and 3 become the front and back walls. The face with 6 dots folds over to become the top.
Thus, the pairs of opposite faces are:
1 is opposite 2.
3 is opposite 5.
4 is opposite 6.
Note: This is not a standard die where opposite faces sum to 7.
2. Analyzing the Assembly (Image Y):
There appears to be a contradiction in the problem statement. For example, the leftmost cube (L) shows a top face of 6 and a front face of 4. According to our net, faces 4 and 6 are opposite and cannot be adjacent on a cube. Similarly, the top cube (T) shows top=1 and front=5, but in our net, these are not adjacent.
Given these contradictions, a direct logical deduction is impossible. The problem is likely flawed. However, in an exam context, we must attempt to find the intended logic. The contradiction may be a mistake, and we should proceed by applying the "opposite faces" rule to the front faces to find the rear faces, as this is the most common logic in such puzzles.
3. Deducing Rear Faces (assuming the Front Views are correct and the Opposite-Face rule applies):
Let's find the rear face for each cube in Image Y. The rear face is opposite the front face.
Top Cube (T): Front face is 5. Opposite of 5 is 3. Rear face should be 3.
Middle Cube (M): Front face is 5. Opposite of 5 is 3. Rear face should be 3.
Bottom Cube (B): Front face is 3. Opposite of 3 is 5. Rear face should be 5.
Left Cube (L): Front face is 4. Opposite of 4 is 6. Rear face should be 6.
Right Cube (R): Front face is 4. Opposite of 4 is 6. Rear face should be 6.
This result (Rear view: T=3, M=3, B=5, L=6, R=6) does not match any of the options. This confirms the problem is ill-posed.
Let's assume the Answer Key (D) is correct and see if any alternative logic could lead to it.
Answer (D) shows the rear view as: T=2, M=5, B=4, L=2, R=3. This does not follow any consistent rule based on the provided net.
Due to the internal contradictions in the question's diagram, a valid solution cannot be derived. We present the answer from the answer key.
Step 4: Final Answer:
The problem statement contains contradictions that make it logically unsolvable. However, based on the provided answer key, the correct option is (D).
