MathDB

Let us consider mathematical crossword which we fill with numbers

0

1

2

3

4

5

6

7

8

9

such that: 1) All digits occur exactly twice 2)

10

horizontally divides

4

vertically 3)

4 \cdot

(

4

horizontally -

4

vertically +

5

) equals

1

vertically 4)

36

divides

1

horizontally and

5

vertically 5)

9

vertically divides

5

vertically
In how many ways we can solve this mathematical crossword?
https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOC85LzgyNjUzYmNkNTVmNDE1YTg4OWVkNzAzYzE1M2JkZWE0MThiYWY1LnBuZw==&rn=Y3Jvc3N3b3JkLnBuZw==

Problem Statement