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Question

Make 0246891357 from 0123456789 using

only two permutations P1 and P2 where

P1 is a left circular shift and P2 is

flipping the elements in the first two

pairs. Specifically, P1 will transform

ABCDEFGHIJ into BCDEFGHIJA, and P2 will

transform ABCDEFGHIJ into BADCEFGHIJ.

Use the fewest possible number of moves

where a move consists of an application

of either P1 or P2.

Here's an example which shows a way to

make 0817923456 from 0123456789:


0123456789 Starting position
7890123456 P1 applied 7 times
8709123456 P2
7091234568 P1
0719234568 P2
8071923456 P1 applied 9 times
0817923456 P2
[/code]

for a total of 20 moves.

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20 moves

P2 1032456789

P1 0324567891

P2 3042567891

P1 0425678913

P1 4256789130

P1 2567891304

P1 5678913042

P2 6587913042

P1 5879130426

P2 8597130426

P1 5971304268

P2 9517304268

P1 5173042689

P2 1537042689

P1 5370426891

P2 3507426891

P1 5074268913

P1 0742689135

P2 7024689135

P1 0246891357

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