Code and ciphers: Julius Caesar, the Enigma and the internet

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solutions to problems
The solution is
SOLVING THIS IS EASY
The numbers of correct plaintext letters appearing in the six rows are
seen to be
0, 3, 5, 8, 4, and 0
These agree fairly well with what we would expect from the theoretical
key distribution which predicts that, in a sufficiently long text, the ratios
should be
1:5:10:10:5:1.
10.2 (Hagelin cages)
All but cages (b) and (e) generate all key values (mod 26). Cage (b) fails to
generate key values 13 and 14. Cage (e) fails to generate key values 4, 12,
15 and 23. Note that if an unoverlapped cage which uses 27 lugs fails to
generate key value N it must also fail to generate key value (27�N) since
the kicks add up to 27 and by reversing the pins on the wheels a key value
of N becomes a key value of (27�N).
10.3 (Overlapped Hagelin cage producing key value 17)
There is unfortunately no short cut to finding these representations
although we can reduce the number of pin combinations that we need to
examine by noting that one, and only one, of the two ‘big’ kicks (11, 9)
will be required, since together they give 18 (ie 11�9�2), and the other
four (7, 5, 3 and 1) only add up to 16, and overlaps would reduce this
further. We need therefore consider only 32 of the 64 possible pin combinations.
The six combinations which produce key value 17 are:
OXXOXO which gives (9�7�3)�(2)�17;
OXXOXX which gives (9�7�3�1)�(2�1)�17;
OXXXOO which gives (9�7�5)�(2�2)�17;
XOOXOX which gives (11�5�1)�(0)�17;
XOOXXO which gives (11�5�3)�(2)�17;
XOOXXX which gives (11�5�3�1)�(2�1)�17.