The Fifteen Puzzle and $S_n$

Question

I was studying permutation groups from the book "Abstract Algebra and Applications" by Karlheinz Spindler in which page 553 I came across the following interesting problem. It is on the famous "The Fifteen Puzzle" for which I am unable to upload the picture but rather I would try to use mathematical notation.

Imagine the fifteen puzzle grid is being presented by the following $4\times 4$ matrix given by $$\left[\begin{matrix} 1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12\\ 13 & 15 & 14 & \circ \end{matrix}\right]$$ where $\circ$ is the empty place in the grid. We can slid the "numbered tiles" through blank space and are supposed to bring down the final structure as $$\left[\begin{matrix} 1 & 2 & 3 & 4\\ 5 & 6 & 7 & 8\\ 9 & 10 & 11 & 12\\ 13 & 14 & 15 & \circ \end{matrix}\right]$$

Now the questions are enter image description here

Can some one tell me exactly what am I supposed to do now to solve the problem ?

Older post: What is the parity of permutation in the 15 puzzle? — Martin Sleziak, Jun 17 '15 at 12:37
There are also post on 8 puzzle: How to check if a 8-puzzle is solvable? — Martin Sleziak, Jun 17 '15 at 12:39
The book (at least this edition) also says: "Hint. Use (22.12)(e)." This is the claim that: "If $n\ge3$ then $\mathrm{Alt}_n$ is generated by all cycles $(1,2,k)$ with $3 \le k \le n$." — Martin Sleziak, Jun 17 '15 at 12:53
The non-accepted answer to the older post contains some useful information for this question, but this question is not a duplicate (despite two votes to close it as such). — Brian M. Scott, Jun 17 '15 at 18:14
The first task is to understand what it means for permutations in $S_n$ (or more specifically in $S_{15}$) to be "even". I can't tell if defining this for the OP is part of "tell me exactly what am I supposed to do now to solve the problem". — hardmath, Jun 17 '15 at 22:39
I know what is $S_n$ but after going through the entire question, I was blank to understand the situation. So I post here for help — KON3, Jun 18 '15 at 02:45

The Fifteen Puzzle and $S_n$

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