Figure out how to calculate a check digit

[waldoj]

The SCC sometimes provides a 7-digit ID, sometimes an 8-digit ID. It turns out that the eighth digit is a checksum. This is the SCC's code to calculate that checksum but, unfortunately, it's written in Natural. So we've got to figure out Natural sufficiently to recreate the code in Python.

[waldoj]

It looks to me like is done as follows:

1. If the first character is a letter, calculate it as 8.
2. Add up the odd positions. (The 1st character, the 3rd character, etc.)
3. Iterating through each of the even positions and:
   • multiplying it by 2
   • if the result is 2 digits, splitting it into two numbers (e.g., 12 becomes 1 and 2), and adding them together (e.g., 3).
4. Add all of those together.
5. Subtract that number from 100.
6. The least significant digit is the checksum.

I have not tested this.

[waldoj]

So, for example, 0431899.

0 + 3 + 8 + 9 = 20.

4 * 2 = 8
1 * 2 = 2
9 * 2 = 18 = 1 + 8 = 9

20 + 8 + 2 + 9 = 39

100 - 39 = 61

The checksum is 1.

...but the checksum is 4. So, that didn't work.

[CountCulture]

Got this working in Ruby:
https://gist.github.com/CountCulture/0dae80c19f8160159a9d

[waldoj]

Oh, wonderful. I'll compare notes and see where my logic is wrong. :) Thank you!

[waldoj]

OK, take two, with the addition of a new second step:

1. If the first character is a letter, calculate it as 8.
2. Move the last character to the second position.
3. Add up the odd positions. (The 1st character, the 3rd character, etc.)
4. Iterating through each of the even positions and:
   • multiplying it by 2
   • if the result is 2 digits, splitting it into two numbers (e.g., 12 becomes 1 and 2), and adding them together (e.g., 3).
5. Add all of those together.
6. Subtract that number from 100.
7. The least significant digit is the checksum.

So, for example, 0431899.

0943189

0 + 4 + 1 + 9 = 14

9 * 2 = 18 = 1 + 8 = 9
3 * 2 = 6
8 * 2 = 16 = 1 + 6 = 7

14 + 9 + 6 + 7 = 36

100 - 36 = 64

The checksum is 4.

Great, so that worked. Let's try with another one: F004214

8004214

8400421

8 + 0 + 4 + 1 = 13

4 * 2 = 8
0 * 2 = 0
2 * 2 = 4

13 + 8 + 0 + 4 = 25

100 - 25 = 75

The checksum is 5. Bingo.