# The Special Fish Report

## Albert W. Small (December 1944)

### Page 27

Tony Sale's
Codes and Ciphers

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CX/MSS
TOP SECRET Special Fish Report Page 27

Thus a wheel-breaking run on Colossus is merely a means of

converging into a pattern from any given data, by crude convergence, and

using Colossus as a rapid adding machine.

It is necessary at this time to describe the decibanning of a

wheel-breaking run.

Let: r = total number of values of Delta-Z ipj looked at in converging
one given character of the unknown wheel.

r/2 + x/2 = number of dots counted.

r/2 - x/2 = number of crosses counted.

x = excess of dots over crosses.

Therefore "x" is the score given in the wheel-breaking run: the "pippage"

for any given character of the unknown wheel.

Now the factor that the wheel was originally a dot in the

character giving the score x, are estimated as:

Therefore (r+x)/(r-x) is the "value of a pip" (numerically) for that particular

character of the wheel.

It is impossible to evaluate this for each character each time;

so the average value may be considered as an estimate:

R + X
R - X

wherein R = Sum ri or the total number of letters looked at in the whole run;

end X = Sum |xi| if we assume the best possible score to be the true score.

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