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Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.
How many tiny cubes will be formed having one portion white and one portion green for sure?
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Two adjacent portions of a big cube are varnished in green and their r...
To solve the problem of finding how many tiny cubes have one portion white and one portion green, we first need to understand the structure of the big cube and how it's divided.

Understanding the Big Cube
The big cube is segmented into 125 tiny cubes. Since 125 is \(5^3\), this indicates that the big cube has dimensions of \(5 \times 5 \times 5\).

Coloring of the Cube Faces
- Two adjacent faces are varnished green.
- The opposite two faces are varnished white.
- The remaining two faces are varnished blue.

Identifying Tiny Cubes with One Green and One White Face
To find tiny cubes that have one green face and one white face, we focus on the edges where the green and white faces meet:
- The edges connecting green and white faces will contain the tiny cubes of interest.
- Each edge where a green face meets a white face will have **3 tiny cubes** (excluding the corners).

Counting the Edges
- There are **3 edges** connecting the green and white faces:
1. Edge between the first green face and the first white face.
2. Edge between the first green face and the second white face.
3. Edge between the second green face and the first white face.

Calculating the Total
- Each edge contributes **3 tiny cubes**:
\[
3 \text{ cubes/edge} \times 3 \text{ edges} = 9 \text{ tiny cubes}
\]

Conclusion
Thus, the total number of tiny cubes that have one portion white and one portion green is **9**. This effectively captures the interaction between the colored faces of the cube based on the given conditions.
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Two adjacent portions of a big cube are varnished in green and their respective opposite two portions are varnished in white and the rest of the two portions are varnished in blue. The cube is segmented into 125 tiny and equal cubes.How many tiny cubes will be formed having one portion white and one portion green for sure?
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