The surface of a cube is painted red and blue, 3 sides of each color. the cube is then cut into 27 equal sized smaller cubes.

A: How many cubes have at least 2 sides painted blue?

B: How many cubes have at least 1 side painted red?

To answer these questions, we first need to understand how the original cube is painted.

The surface of the cube is divided into 6 sides. Three sides are painted red, and the other three sides are painted blue. This means that each color covers half of the total surface area of the cube.

Now, let's move to answering the questions.

A: How many cubes have at least 2 sides painted blue?

To determine this, we need to consider the cubes within the larger cube. We can visualize these smaller cubes as being arranged in a 3x3x3 grid, with a total of 27 smaller cubes.

Since half of the surface area of the original cube is painted blue, we can infer that half of the smaller cubes will have at least 2 sides painted blue. In other words, there will be 13.5 cubes with at least 2 sides painted blue.

However, since we cannot have a fraction of a cube, we need to round this number to the nearest whole number. In this case, since we have 13.5 cubes, we round it down to 13 cubes.

Therefore, there are 13 cubes with at least 2 sides painted blue.

B: How many cubes have at least 1 side painted red?

Since half of the surface area of the original cube is painted red, we can similarly infer that half of the smaller cubes will have at least 1 side painted red.

Therefore, there will be 13.5 cubes with at least 1 side painted red.

Again, rounding this number to the nearest whole number, we get 13 cubes.

Therefore, there are 13 cubes with at least 1 side painted red.