data/problems/336.yml
---
:id: 336
:name: Maximix Arrangements
:url: https://projecteuler.net/problem=336
:content: "A train is used to transport four carriages in the order: ABCD. However,
sometimes when the train arrives to collect the carriages they are not in the correct
order. \nTo rearrange the carriages they are all shunted on to a large rotating
turntable. After the carriages are uncoupled at a specific point the train moves
off the turntable pulling the carriages still attached with it. The remaining carriages
are rotated 180 degrees. All of the carriages are then rejoined and this process
is repeated as often as necessary in order to obtain the least number of uses of
the turntable. \nSome arrangements, such as ADCB, can be solved easily: the carriages
are separated between A and D, and after DCB are rotated the correct order has been
achieved.\n\nHowever, Simple Simon, the train driver, is not known for his efficiency,
so he always solves the problem by initially getting carriage A in the correct place,
then carriage B, and so on.\n\nUsing four carriages, the worst possible arrangements
for Simon, which we shall call _maximix arrangements_, are DACB and DBAC; each requiring
him five rotations (although, using the most efficient approach, they could be solved
using just three rotations). The process he uses for DACB is shown below.\n\n \n\nIt can be verified that there are 24 maximix
arrangements for six carriages, of which the tenth lexicographic maximix arrangement
is DFAECB.\n\nFind the 2011<sup>th</sup> lexicographic maximix arrangement for eleven
carriages.\n\n"