# The Newmanry History

## Part of the General Report on Tunny (1945)

### Page 350

Tony Sale's
Codes and Ciphers

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53M Page 350

(i) Carriage return is operated only after the completion of a row.

(ii) settings are not printed.

(iii) A score is printed as a single figure.

On Colossus 6 scores exceeding 9 are represented by letters viz. A = 10, B =
11 and so on.

(c) Multiple Test in Rectangling.

To increase the speed of rectangling, multiple testing on X1 is used.
Multiple testing always examines batches of settings whose "present" member
belongs to the sequence 1,6,11.......41. The first batch of settings in each row
of the rectangle is chosen to be 02 - 06, 06 being "present", 02,03,04,O5
"remembered". In order that X2 shall step at the correct position of X1, the X1
setting plug must be at 01. If however X1 were actually set at 01, the first row
would begin with settings 38, 39, 40, 41, 01. To make the first row begin 02,
03, 04, 05, 06 the wheels are set with the X1 plug at 06 : the plug is then
returned to 01 without resetting.

Because the rectangle is made backwards the first five readings should be
for the last five cells of the rectangle, which contain places of the cipher whose
remainders on division by 41 an 37, 38, 39, 40, 41 so that the required
differences (Delta-Z1) are 37 + 38, 38 + 39, 39 + 40, 40 + 41, 41 + 01. Since
Colossus differences backwards, the cross in X1 must be against cipher places
38,39,40,41,01. The first batch of settings is 02,03,04,05,06; and therefore the
cross must be in position 02:

X2 has a cross in 02, for symmetry, and it follows that its setting is 02.

The last batch of settings is 38,39,40,41 and 01 of which 38,39, 40,41
are also in the last batch but one: the rectangle gadget prevents these from being
printed twice.

(d) Print Scores

Done thus, the rectangle would have to be done twice, for Delta-Z1 + Delta-
Z2 = ., and for Delta-Z1 + Delta-Z2 = x. Conditional rectangles are done this
way; the rectangling switch is thrown to "print scores".