The surface of a cube is painted red and blue, 3 sides of each. The cube is cut into 27 equal sized smaller cubes. Find both answers to the question, "How many cubes have at least 2 sides painted blue?" and "How many cubes have at least 1 side painted red?"

I attempted it but still don't get how to do it. Please be very specific when explaining.

To find the answers to these questions, we need to break down the problem step by step.

Step 1: Understand the problem:
- We have a cube that has 6 faces.
- Each face is painted with a combination of red and blue, with 3 sides of each color.

Step 2: Visualize the cube:
To make it easier to understand the problem, let's visualize the original cube. Imagine each face as a 3x3 grid and label the sides as R (red) or B (blue).

RRR
RRR
RRR
BBB BBB BBB BBB
BBB BBB BBB BBB
BBB BBB BBB BBB
RRR
RRR
RRR
RRR

Step 3: Divide the cube into smaller cubes:
We are given that the original cube is divided into 27 equal-sized smaller cubes. We can imagine this as a 3x3x3 cube composed of 27 identical smaller cubes.

Step 4: Count cubes with at least 2 sides painted blue:
To determine how many cubes have at least 2 sides painted blue, we can focus on the corners of the 3x3x3 cube. These corners consist of 8 smaller cubes each.

RRR
RRR
RRR
BBB BBB BBB BBB
BBB BBB BBB BBB
BBB BBB BBB BBB
RRR
RRR
RRR
RRR

There are 8 corners, and each corner has 8 smaller cubes (since each corner is shared by 8 bigger cubes surrounding it). So, there are 8 x 8 = 64 smaller cubes in the corners. And since each smaller cube has 3 sides painted blue, those 64 cubes would cover 64 x 3 = 192 sides painted blue.

Step 5: Count cubes with at least 1 side painted red:
To determine how many cubes have at least 1 side painted red, we need to consider the face cubes (not the corners). In each face, there are 3 x 3 smaller cubes, totaling 9 smaller cubes per face. Since there are 6 faces, the face cubes would cover 9 x 6 = 54 smaller cubes in total. And since each smaller cube has 3 sides painted red, these 54 cubes would give us 54 x 3 = 162 sides painted red.

So, the final answers are:
- The number of cubes with at least 2 sides painted blue is 192.
- The number of cubes with at least 1 side painted red is 162.