Problem #PRU-98400

Problems Discrete Mathematics Set theory and logic Set theory Inclusion-exclusion principle

Problem

A cube with side length of 20 is divided into 8000 unit cubes, and on each cube a number is written. It is known that in each column of 20 cubes parallel to the edge of the cube, the sum of the numbers is equal to 1 (the columns in all three directions are considered). On some cubes a number 10 is written. Through this cube there are three layers of 1×20×20 cubes, parallel to the faces of the cube. Find the sum of all the numbers outside of these layers.