Staffan rather quickly managed to pair the columns two and two to form a new code matrix with only four columns. We now knew these actually represented letters in a 64 character alphabet. The problem was now reduced to finding out which of the possible 24 permutations that was the correct one.
Staffan wrote an interactive program for simultaneously testing replacements in all the 24 possible solutions, and the problem was reduced to a substitution cipher. The problem was to know which one of the ciphertexts to focus on. We hoped that as soon as we got a few characters in place, it would become apparent which one was the correct text. However, the problem did not yield as easily to that approach as we had first thought.
After thinking a couple of days, we focused on the fact that the first four characters would always be the same, and only the order of them would vary. By using the classic technique of frequency analysis, we observed the first four characters' relative frequency.
With this data, we looked at frequencies for different languages and somehow guessed that German seemed to be the only language that could probably satisfy these frequencies and their connection. This also fit quite well with the fact that the ADFGVX cipher was used by Germany during the first world war. Once that guess was made, it was rather easy to deduce which of the 24 alternative crypto-texts was the correct one.
From that on, the rest of the solution was just a simple matter of replacing characters interactively and the whole text was open in a couple of minutes.
In this process, we realized that we recognized the plaintext and pulled out a copy of Fermat's Last Theorem to fill in the blanks. Close to the end of text we found the keyword, EDISON, followed by a very interesting paragraph:
Der naechste Teil enthaelt eine von einer Enigmamaschine verschluesselte Mitteilung. Die Abbildung zeigt die Verbindungen innerhalb jeder Walze und der Umkehrwalze der Maschine. Es ist dennoch zu beachten dass das Walzenlage falsch wiedergegeben ist. Eigentlich sollen Walze 1 und Walze 2 gegeneinander ausgetauscht werden. Die urspruengliche Walzestellung und Ringstellung und Steckerverbindungenstellung sind unbekannt.
Thus spurred by the success in solving the seventh stage, we also jumped to re-running Stage 8, which was attacked in parallel with this stage, armed with the new information that was revealed to us in the plaintext of Stage 7. We started a full run of analysis for Stage 8 with the new information, hoping to crack that one too.
However, Stage 8 still did not yield. At this point, Stages 6-8 had been worked on in parallel, and we hoped that the success with this stage would soon be followed by Stages 6 and 8 yielding. This was also what happened.