To solve this problem, we need to understand the structure of the cube and how it is divided into smaller cubes.

First, let's consider the original cube. It has 6 faces, and we painted two pairs of opposite faces with yellow and orange, respectively, while the remaining faces are white. This means that each pair of opposite faces has the same color.

Now, let's think about how the cube is divided into smaller cubes. The cube is cut into 343 identical smaller cubes, which means it is divided into a 7x7x7 grid of smaller cubes. Each side of the original cube is divided into 7 equal segments, resulting in 49 smaller cubes on each face.

To determine how many of the smaller cubes have exactly one color on them, we need to consider the different possibilities.

1. Smaller cubes with only yellow color:
Since we painted two pairs of opposite faces yellow, there are 49 smaller cubes on each of these faces that have only yellow color.

2. Smaller cubes with only orange color:
Similarly, there are 49 smaller cubes on each of the faces painted orange that have only orange color.

3. Smaller cubes with only white color:
The remaining faces of the original cube are painted white. Since each face has 49 smaller cubes, there are a total of 49 x 4 = 196 smaller cubes that have only white color.

Therefore, the total number of smaller cubes that have exactly one color on them is:
49 (yellow) + 49 (orange) + 196 (white) = 294 smaller cubes.

So, there are 294 smaller cubes that have exactly one color on them.

Question

To solve this problem, we need to understand the structure of the cube and how it is divided into smaller cubes.

First, let's consider the original cube. It has 6 faces, and we painted two pairs of opposite faces with yellow and orange, respectively, while the remaining faces are white. This means that each pair of opposite faces has the same color.

Now, let's think about how the cube is divided into smaller cubes. The cube is cut into 343 identical smaller cubes, which means it is divided into a 7x7x7 grid of smaller cubes. Each side of the original cube is divided into 7 equal segments, resulting in 49 smaller cubes on each face.

To determine how many of the smaller cubes have exactly one color on them, we need to consider the different possibilities.

1. Smaller cubes with only yellow color: 
Since we painted two pairs of opposite faces yellow, there are 49 smaller cubes on each of these faces that have only yellow color.

2. Smaller cubes with only orange color: 
Similarly, there are 49 smaller cubes on each of the faces painted orange that have only orange color.

3. Smaller cubes with only white color: 
The remaining faces of the original cube are painted white. Since each face has 49 smaller cubes, there are a total of 49 x 4 = 196 smaller cubes that have only white color.

Therefore, the total number of smaller cubes that have exactly one color on them is:
49 (yellow) + 49 (orange) + 196 (white) = 294 smaller cubes.

So, there are 294 smaller cubes that have exactly one color on them.

Knowee AI · Accepted Answer