So I found a small issue with my code that I need to fix. The fix is incredibly easy but took hours to figure out. I was making up some materials for a YouTube video explaining how the system works, when I realized that something not quite right. When you have a 5 digit code with 5 keys, there are **3125 different codes to test**. The DeBrujin sequence is 100% efficient at reusing past digits, so I am supposed to be testing a full 5 digit code with each keypress. Yet I realized something. **The first four keypresses are not actually testing a code** because you haven't completed entering a five digit code until you've pressed five digits. So since the first four digits are wasted,** it should take 3129 keypresses** to test all 3125 codes. Something is not quite right here, since there are only **3125 digits in the sequence** output by the python code I found on Wikipedia.

So apparently **I am not testing 4 of the possible codes**. After a bit of puzzling about how this could be possible I gave up and decided to brute force figure out which ones were missing. I altered the Wikipedia code to output each digit followed by a newline so I could import into rows in Libreoffice Calc. I wrote a formula to create a column with each code that is tested by each digit - stripping the left digit and adding the new digit to the right end. Then I wrote another piece of code to generate a list of all possible codes. I pasted that list into the spreadsheet and wrote a lookup formula to indicate if each one was found in the first list generated by the sequence. ** It found four missing codes.**

When I looked at the four codes that were missing **it suddenly became evident what was going on**. The four codes are **91111, 99111, 99911, and 99991**. I looked for where these should be in the sequnce and noticed that the sequence **ends with five nines and starts with five ones**. To actually finish the sequence you have to **connect the end to the beginning and continue for four more digits**. Those first four digits that don't test anything would be testing the four missing codes if you were **continually going around the sequence in a circle**.

So all I have to do to fix the problem **is add four nines to the start or four ones to the end** of the sequence and it will test those four missing codes. I haven't updated the code yet but I know it will work fine when I do. Someday I'll get around to uploading the code to the project page. And making those YouTube videos...

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