On October 19th we were put on our feet again by a piece of good fortune of the type which saved us on so many occasions; in the confusion which followed the retreat from France and the fighting in Belgium and Holland, one Bonito group got stranded with no keys but Dolphin and the result was a spate of reencodements. These did not last very long, but they gave us time to examine the traffic for cribs and find the position much improved. First of all weather cribs and later situation reports kept Bonito under control for the rest of the war; December 24th and 25th and January 5th and 6th 1945 are the only missing days until the last 2 days of April.
DIGRESSION ON WHEEL ORDER RULES
The discovery of Wheel Order Rules reflects very little credit on Hut 8. Most of the work was done in May 1944 at Op-2O-G by Lt. Commander Church and his assistants. There is no doubt that we had paid insufficient attention to the study of wheel orders and by our failure had wasted a considerable amount of bombe time in the past.
Certain wheel order rules were known. Every wheel order had to contain a 6, 7 or 8; these being the most recent wheels it was presumably hoped that we had not captured them. This reduced the number of possible wheel orders from 336 to 276.
We had noticed also, indeed we could hardly have failed to do so, the extreme rarity of crashing wheel orders, i.e., wheel orders using the same wheel in the same place 2 days running; thus 2, 7 and 6 followed by 3, 7 and 1 was most unlikely but there was no objection to 2 7 6 followed by 6 1 7. In fact crashing wheel orders were never worth considering until very heavy factor had been put against non-crashers.
Certain other wheel order rules had been exploited. We had flirted with an extraordinary and doubtless bogus system known as 'anagram wheel orders' and in 1942 good cribs were run on 'Wylie wheel orders' if there was a mild flap on; Wylie wheel orders assumed that none of the 3 wheels used in one day's wheel order were used in the next and had a fairly small factor in their favour. A more useful discovery were 'Bog wheel orders'. It appears that the German key-maker crossed off wheel orders as he used them and did not reuse them for the batch of keys he was composing; he seems to have made up wheel orders for one key at a time and to have done about 6 months at a stretch. By the end of a Bog period a considerable number of wheel orders were saved, but the rule was a treacherous one and it was difficult to estimate accurately the factor against Bogs at any time.
The 1944 discoveries were of a completely different class from these rather precarious limitations. The new rules were based simply on a study of the order and frequency of use of left hand wheels and the conclusions were supported by the intrinsic probability and comprehensibility of the system. The idea implicit in
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