1. A complete number is a 9-digit number that contains each of the digits 1 through 9 exactly once. Furthermore, the difference number of a number $N$ is the number you get when you take the difference of each pair of adjacent digits in $N$ and concatenate all these differences. For example, the difference number of 25143 is 3431. The complete number 124356879 has the additional property that its difference number 12121212 alternates between the digits 1 and 2.

Determine all $a$ with $3 \leqslant a \leqslant 9$ for which there exists a complete number $N$ with the additional property that the difference number of $N$ alternates between the digits 1 and $a$.
## 1. Version for class $5 \&$ class 6

In the solutions for class 4 and lower, you can see that this is possible for $a=4$ and $a=5$ and impossible for all other $a$.