permutations used for the indicator. The Poles would then use the grill method to determine the rightmost rotor and its position. That search would be complicated by the plugboard permutation, but that permutation only swapped six pairs of letters — not enough to disrupt the search. The grill method also determined the plugboard wiring. The grill method could also be used to determine the middle and left rotors and their setting (and those tasks were simpler because there was no plugboard), but the Poles eventually compiled a catalog of the possible permutations (reflector and 2 leftmost rotor permutations), so they could just look up the answer. The only remaining secret of the daily key would be the ring settings, and the Poles would attack that problem with brute force. Most messages would start with the three letters "ANX" (an is German for "to" and the "X" character was used as a space). It may take almost trials, but that was doable. Once the ring settings were found, the Poles could read the day's traffic. The Germans made it easy for the Poles in the beginning. The rotor order only changed every quarter, so the Poles would not have to search for the rotor order. Later the Germans changed it every month, but that would not cause much trouble, either. Eventually, the Germans would change the rotor order every day, and late in the war (after Poland had been overrun) the rotor order might be changed during the day. The Poles kept improving their techniques as the Germans kept improving their security measures. Invariant cycle lengths and the card catalog Rejewski realised that, although the letters in the cycle groups were changed by the plugboard, the number and lengths of the cycles were unaffected—in the example above, six cycle groups with lengths of 9, 9, 3, 3, 1 and 1. He described this invariant structure as the characteristic of the indicator setting. There were only 105,456 possible rotor settings. The Poles therefore set about creating a card catalog of these cycle patterns. The cycle-length method would avoid using the grill. The card catalog would index the cycle-length for all starting positions (except for turnovers that occurred while enciphering an indicator). The day's traffic would be examined to discover the cycles in the permutations. The card catalog would be consulted to find the possible starting positions. There are roughly 1 million possible