These were simply tables of all the core-positions, in which instead of printing 'has a female' or 'has no female', there would either be a hole punched, or not.
In principle they could first have constructed one such huge table, and then each day could have made a template with the pattern of females observed in the traffic of that day.
Passing the template over the table, they would eventually have found a position where the holes matched.
But that would have been far too inefficient a method.
Instead, they had a method of piling pieces of the table of core positions on top of each other, staggered in a manner corresponding to the observed relative positions of the females.
A 'matching' of the pattern would then show up as a place where light passed through all the sheets.
The advantage of this staggering system was that 676 possibilities could be examined simultaneously.
It was still a long job, requiring 6 × 26 operations for a complete search.
It also required the construction of perforated sheets listing the 6 × 17576 core-positions.
Yet they achieved this within a few months.
This was not the only method they devised. The perforated sheet system required the location of about ten females in the traffic.
A second system required only three, but it used not only the mere existence of a female, but the particular letter that appeared as female in the cipher-text.
It was essential to the principle of the method that these particular letters had to be among those left unaffected by the plugboard.