What I found: 753 7512 762 7152 34152 3417 357 That's the same as your solution but in reverse. It's not possible in 4 steps or less, because if you ignore t

What I found: 753 7512 762 7152 34152 3417 357 That's the same as your solution but in reverse. It's not possible in 4 steps or less, because if you ignore the no-duplicates-rule, there is only 1 possibility and that one has duplicates. It's not possible in 5 steps, because you would not end up with an odd length list again. Solutions will always have an even number of steps. So six must be shortest.