cycle-length combinations and only 105,456 starting positions. Having found a starting position, the Poles would use an Enigma double to determine the cycles at that starting position without a plugboard. The Poles would then compare those cycles to the cycles with the (unknown) plugboard and solve for the plugboard permutation (a simple substitution cipher). Then the Poles could find the remaining secret of the ring settings with the ANX method. The problem was compiling the large card catalog. Rejewski, in 1934 or 1935, devised a machine to facilitate making the catalog and called it a cyclometer. This "comprised two sets of rotors... connected by wires through which electric current could run. Rotor N in the second set was three letters out of phase with respect to rotor N in the first set, whereas rotors L and M in the second set were always set the same way as rotors L and M in the first set". Preparation of this catalog, using the cyclometer, was, said Rejewski, "laborious and took over a year, but when it was ready, obtaining daily keys was a question of [some fifteen] minutes". However, on 1 November 1937, the Germans changed the Enigma reflector, necessitating the production of a new catalog—"a task which [says Rejewski] consumed, on account of our greater experience, probably somewhat less than a year's time". This characteristics method stopped working for German naval Enigma messages on 1 May 1937, when the indicator procedure was changed to one involving special codebooks (see German Navy 3-rotor Enigma below). Worse still, on 15 September 1938 it stopped working for German army and air force messages because operators were then required to choose their own Grundstellung (initial rotor setting) for each message. Although German army message keys would still be double-enciphered, the day's keys would not be double-enciphered at the same initial setting, so the characteristic could no longer be found or exploited. Perforated sheets Although the characteristics method no longer worked, the inclusion of the enciphered message key twice gave rise to a phenomenon that the cryptanalyst Henryk Zygalski was able to exploit. Sometimes (about one message in eight) one of the repeated letters in the message key enciphered to the same letter on both occasions. These occurrences were called samiczki (in English, females—a term later used at Bletchley Park). Only a limited number of scrambler settings would give rise to females, and these would