It's commonly stated that there is only one solution to the 3x3 magic square. This is simply because every variant found is simply a rotation, reflection or both of any other variant. Once such variant is:
Objective
Now, your goal is to make it less interesting, albeit, in an interesting way. Your objective is simple, rearrange the magic square so that the digits can be read in sequence from $1$ to $9$ starting in the top left corner, to the bottom right corner:
How to Play
To rearrange the tiles, you'll need to swap them, one by one into their correct positions. For example, the $1$ tile can be swapped with the $8$ tile, effectively placing the $1$ tile in its correct position:
However, be very careful on which tiles you swap as there are two important rules to swapping tiles:
- Each tile can only be swapped the number of times its face represents.
- When swapping tiles, the lower face value is deducted from the higher face value's remaining moves.
For clarity, let's use the $8$ tile as an example. At the start, it can be moved 8 times before it becomes locked into place. Swapping it with the $1$ tile reduces the number of times it can be moved going forward to 7. To clarify the second rule, imagine that we now swap the $8$ tile with the $6$ tile:
Two things happen here; the $6$ tile now has $5$ moves remaining, and the $8$ tile now has $1$ move remaining. This isn't optimal because the $8$ tile is nowhere near where it needs to be.
Movement Restrictions
Tiles can be swapped if they are adjacent to each other. Additionally, outside tiles are considered adjacent. Diagonal movements are not allowed. For example, the $8$ tile can be swapped with the $1$, $6$, $3$ and $4$ tiles initially.
Can you remove the magic from a 3x3 magic square?
