We built a structure similar to the one in the picture, but instead of four floors, it had twenty-five. Then we painted all the outer walls of the building. The vertical walls were red and the horizontal walls were blue. (The building stands on the ground, so we did not paint the base.)

a) How many times more red paint did we use than blue?

b) How many walls of the cubes did we paint in total?
It is important to realize that each colored wall of this building can be seen from one of the following views: from the front, from the right, from the back, from the left, and from above (orientation according to

![](https://cdn.mathpix.com/cropped/2024_04_17_5ead866a615c7556f458g-2.jpg?height=326&width=345&top_left_y=248&top_left_x=570)

view from the front

![](https://cdn.mathpix.com/cropped/2024_04_17_5ead866a615c7556f458g-2.jpg?height=274&width=348&top_left_y=297&top_left_x=1211)

view from the back

the walls of the cube at the top of the building). In each of these views, we see the same shape (except for orientation), where all squares (walls) are colored the same color: in the case of the first four views, red, and in the last case, blue. Therefore, we have the answer to the first question: Since the number of red-colored walls is four times the number of blue-colored walls, the consumption of red paint is four times that of blue. In each of the five views, we see \(1+2+3+\ldots+25=325\) walls, so in total, we have colored \(5 \cdot 325=1625\) walls of the cubes.

discovery that in the \(v\) given views, we see the same shape - \(2 b\)

justification for the fourfold consumption of red paint - \(1 b\)

calculation of the number of colored walls of the cubes - \(3 b\)