# Solution

The answer to the first question is

```
x   1  2  3  4  5  6  7  8  9 10
ilog(x)  0  1  4  2  6  5  9  3  8  7

```
The multiplication table is as follows:
```
1   2   3   4   5   6   7   8   9  10
2   4   6   8  10   5   1   3   7   9
3   6   9   5   1   7   8  10   4   2
4   8   5   3   9  10   2   6   1   7
5  10   1   9   4   2   6   7   3   8
6   5   7  10   2   1   3   9   8   4
7   1   8   2   6   3   9   4  10   5
8   3  10   6   7   9   4   5   2   1
9   7   4   1   3   8  10   2   5   6
10   9   2   7   8   4   5   1   6   3

```
I made a program to calculate ilog(x) and its multiplication table in any order N. The solutions (N=2...199) calculated by the program are given in the following files. To display the results of large N, I used a graphic expression in which each number is expressed by the gray scale colors (0 corresponds black, and N, white). The most intriguing thing is that there is no solution in N=195. I do not know the reason, but it is proven by my program which scans all of the cases.