A $20 \times 20 \times 20$ cube is divided into 8000 unit cubes. A number is written in each unit cube. In each row and in each column of 20 small cubes, parallel to one of the cube's edges, the sum of the numbers is 1. In one of the small cubes, the number written is 10. Through this small cube pass three layers $1 \times 20 \times 20$ parallel to the faces of the cube. Find the sum of all the numbers outside these three layers.

## - Solution of the exercises -

 untranslated portion: 

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。

---

A $20 \times 20 \times 20$ cube is divided into 8000 unit cubes. A number is written in each unit cube. In each row and in each column of 20 small cubes, parallel to one of the cube's edges, the sum of the numbers is 1. In one of the small cubes, the number written is 10. Through this small cube pass three layers $1 \times 20 \times 20$ parallel to the faces of the cube. Find the sum of all the numbers outside these three layers.

## - Solution of the exercises -
Let's calculate the sum over the union of the three layers using the principle of inclusion-exclusion. We get $20+20+20-1-1-1+10=67$. The sum of all the numbers in the cube is 400. The final result is therefore $400-67=333$.

## 4 TD

## - Statements -