A cube coated with red surface is divided into several small cubes of equal size, in which there are 218 small cubes with red on 1, 2 or 3 sides of the surface, and how many small cubes without red on the surface are there
According to the inscription, the number of parts of each edge of the original cube after cutting is equal.
3 small red cubes are located at the 8 vertices of the original cube, 2 red cubes are in the edges of the original cube (minus the small cubes on the two vertices on each edge), and 1 red cube is located in the faces of the original cube (minus the small cubes around each face).
Therefore, the total number of small red cubes with 2 or 1 side is: 218-8=210 (pieces).
Assuming that the number of small cubes in each edge is a, the number of small red cubes on two sides is 12 a, and the number of small red cubes on one side is 6 a2.
This gives the equation: 12a+6a2=210
Simplification: 2a+a2=35
Using the multiplicative distributive property, the above equation is variant: a (2+a)=35
Factoring 35 into a factor, we can derive: a=5
So far, green, blue, and red are used to represent the small cubes on the vertices, in the edges, and in the faces, as shown in the following figure
Therefore, the number of small cubes with no red surface (small cubes in the belly of the original cube) is: 5 5 5 = 125 (pieces).
Of course, you can also subtract the number of small cubes with red on 3, 2, and 1 sides from the total number of small cubes, and you can also get the number of small cubes without red.