Which of the options, when combined with block shown on top, will result in perfect 4x4x4 cube?
Show Hint
In 3D block puzzles, instead of trying to visualize the entire complex merge, focus on a simple, unambiguous feature like a hole that goes all the way through or a prominent corner. Use this feature to quickly eliminate most of the incorrect options.
Step 1: Understanding the Concept:
This question is a 3D spatial reasoning puzzle. We need to find the shape (from options A, B, C, D) that is the perfect complement to the red shape, meaning that when the two are joined, they form a solid 4x4x4 cube with no gaps or overlaps.
Step 2: Key Formula or Approach:
The most effective approach is to identify a "negative space" or a hole in the red object and see which of the options has a corresponding "positive space" or solid part to fill it. This is like fitting puzzle pieces together. We can analyze the structure layer by layer or by looking for distinctive features.
Step 3: Detailed Explanation:
Let's analyze the red block to find a clear "hole" that needs to be filled.
Observe the front-left corner of the space where the 4x4x4 cube would be. The red block is completely absent from this corner column. This means there is a 1x1 hole that goes all the way through the structure from top to bottom.
The complementary blue piece must therefore have a solid 1x1 column that is 4 blocks high, located at its corresponding corner (which would be the front-left corner in the given orientation).
Now let's check the options for this feature:
(A) This shape has a pillar at the front-left, but it appears to be only 3 blocks high, not 4.
(B) This shape does not have a 4-block high pillar at any corner.
(C) This shape also does not have a 4-block high pillar.
(D) This shape has a distinct, solid 1x1 pillar that is 4 blocks high at its front-left corner.
Based on this single feature, option (D) is the only possible candidate.
To confirm, we can perform a layer-by-layer check:
Top layer (layer 4): The red block has a 2x2 square (4 blocks). A full layer has 16 blocks. Option (D) has a corresponding L-shape of 12 blocks for this layer (4 + 12 = 16). This fits.
Layer 3: A visual inspection shows that the shapes of the red block and the corresponding layer of block (D) are complementary and would fill a 4x4 grid.
Layer 2: The same complementary relationship holds.
Bottom layer (layer 1): The same complementary relationship holds.
Step 4: Final Answer:
Option (D) is the only shape that perfectly fills the empty space of the red block to create a solid 4x4x4 cube.
