7.5. Vera has 27 cubes with an edge of 1 cm: 9 red and 18 blue. She assembled them into a cube with an edge of 3 cm. Can the number of red squares with a side of 1 cm on the surface of the cube be equal to the number of such blue squares?
Answer: No.

Solution. In total, there are $9 \cdot 6 = 54$ squares on the surface of the resulting cube. Three faces of a small cube will be on the surface if the cube is in a corner, two faces if the cube touches an edge of the large cube, and one face if the cube is in the center of a face. The maximum number of red squares on the surface will occur if 8 red cubes occupy all the corners of the large cube, and one more touches its edge. In this case, there will be $8 \cdot 3 + 2 = 26$ red squares on the surface of the cube, but this is less than $54 / 2 = 27$.

Grading Criteria.

«+» A complete and justified solution is provided

«干» An example is shown where 26 red squares appear on the surface, but there is no explanation of why more cannot be achieved

«-» The problem is not solved or is solved incorrectly