There are 20 possible sequences of 3 letters drawn from the character set
ABCDEF which are in strictly increasing alphabetical order (for instance,
three of these 20 are ABC, ACE, and DEF). Can you give a sequence of these
20 possible sequences such that:
- It begins with ABC and ends with DEF
- The nth sequence is determined by taking the (21-n)th sequence,
and choosing exactly those letters not in that sequence, and putting them
in order
- Neighboring sequences differ by only a single letter, with the exception
of the 10th and 11th sequences (which must have no letters in common, due
to the above requirement)