2. A parallelepiped is composed of white and black unit cubes in a checkerboard pattern. It is known that the number of black cubes is $1 \frac{12}{13} \%$ more than the number of white cubes. Find the surface area of the parallelepiped, given that each side of the parallelepiped is greater than 1.
Solution. The number of black and white cubes can differ by only 1. Therefore, 1 cube is $1 \frac{12}{13} \%$ of the quantity of white cubes. Thus, there are 52 white cubes, 53 black cubes, and a total of 205 cubes. That is, our parallelepiped is $3 \times 5 \times 7$. The surface area is 142.

Answer: 142.

Criteria: 14 points for a justified correct solution. 12 points for a correct solution with an arithmetic error. 6 points for stating that there is 1 more black cube than white cubes. 2 points for the correct answer only.