number of ways that pairs of letters could be interchanged was With L=6, the number of combinations was 100,391,791,500 (100 billion) and with ten leads, it was 150,738,274,937,250 (151 trillion). However, the way that Enigma was used by the Germans meant that, if the settings for one day (or whatever period was represented by each row of the setting sheet) were established, the rest of the messages for that network on that day could quickly be deciphered. The security of Enigma ciphers did have fundamental weaknesses that proved helpful to cryptanalysts. A letter could never be encrypted to itself, a consequence of the reflector. This property was of great help in using cribs—short sections of plaintext thought to be somewhere in the ciphertext—and could be used to eliminate a crib in a particular position. For a possible location, if any letter in the crib matched a letter in the ciphertext at the same position, the location could be ruled out. It was this feature that the British mathematician and logician Alan Turing exploited in designing the British bombe. The plugboard connections were reciprocal, so that if A was plugged to N, then N likewise became A. It was this property that led mathematician Gordon Welchman at Bletchley Park to propose that a diagonal board be introduced into the bombe, substantially reducing the number of incorrect rotor settings that the bombes found. The notches in the alphabet rings of rotors I to V were in different positions, which helped cryptanalysts to work out the wheel order by observing when the middle rotor was turned over by the right-hand rotor. There were substantial weaknesses, in both policies and practice, in the way that Enigma was used (see 'Operating shortcomings' below). Key setting Enigma featured the major operational convenience of being symmetrical (or self-inverse). This meant that decipherment worked in the same way as encipherment, so that when the ciphertext was typed in, the sequence of lamps that lit yielded the plaintext. Identical setting of the machines at the transmitting and receiving ends was achieved by key setting procedures. These varied from time to time and across different networks. They consisted of setting sheets in a codebook. which were distributed to all users of a network, and were changed regularly. The message key was transmitted in an indicator as part of the message preamble. The word key was also used at Bletchley Park