Labyrinths of the World: Fool’s Gold is an AVG game from Domini Games and released by BigFish. The 4th minigame named Clurichaun is really nice.
Arrange sequence using auxiliary slots Puzzle

Arrange sequence using auxiliary slots:
Move each center token to the slot whose path leads to their match. Use the side sword arrows to move the sword. Select the center arrow to move tokens in and out of the sword slots. Tokens light up when placed correctly.

Let’s denote center tokens as number 1~8 from left to right. The pattern of sequence of these tokens can be seen as an integer. So the puzzle can be thought as:

Change a given number(1234567800) to the target number(6345281700) through a series of moves, each move substitutes two adjacent digits in the number with digits in 2 auxiliary slots (denoted as 0).

The Official Walkthrough gives a solution as: {6, 1, 6, 2, 4, 2, 3, 7, 6, 3, 2, 6, 5, 2}, 14 steps in total.

Well, DFS (Depth First Scan) found out the only best solution, 9 steps in total:
{1, 6, 7, 6, 4, 3, 6, 5, 1}
1234567800 => 0034567812 => 0034512867 => 0034516728 => 0034528716 => 0031628745 => 0045628731 => 0045631728 => 0045281763 => 6345281700