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We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic:

Objective

Your objective is simple, rearrange the square so that it becomes a valid 4x4 magic square once more:

How to Play

To rearrange the tiles, you'll need to swap them, one by one into their correct positions. For example, the $8$ tile can be swapped with the $1$ tile to effectively place the $1$ tile in a correct position:

However, be very careful on which tiles you swap as there are two important rules to swapping tiles:

1. Each tile can only be swapped the number of times its face represents.
2. 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 $4$ tile:

Two things happen here; the $4$ tile now has 3 moves remaining, as does the $8$ tile. Now, assume you want to swap the $8$ tile with the $6$ tile; in this scenario you can't because $8$ doesn't have 6 moves remaining, it only has 3 because you swapped with the $1$ and $4$ tiles already.

Movement Restrictions

Tiles can be swapped if they are adjacent to each other. Reactivating magic squares is a much more tedious process than deactivating them; as such, outside tiles are not considered adjacent. Diagonal movements are not allowed. As an example, the $4$ tile can be swapped with the $6$, $1$, $3$ and $13$ tiles initially, but no others:

_{Yes, I've created an interactive version of this puzzle. It will be available to the public (linked here) after this puzzle has an accepted answer.}

Clarifications

Does it have to become the magic square you showed? Or is any 4x4 magic square acceptable?

Any valid magic square is acceptable, though answers that don’t use the provided square should explain why they used a different square.

Suppose we're in a position where $8_3$ is next to $4_4$. Is it true to say that "both have moves remaining so they can be swapped" (which would result in all of 8's moves being used and possibly a debt/negative balance afterwards) or "$8_3$ cannot afford to pay the extra penalty, so cannot move at all"?

$8_3$ cannot afford to pay the extra penalty, so you cannot move at all.

Hints

The initial configuration should not be able to be rearranged into the provided valid magic square. This is due to the second row in particular. Instead, you'll need to determine if a new magic square can accommodate the initial configuration, based on known limitations. For example, the $1$ tile only gets 1 move, so it can only be in 1 of 4 positions in the completed grid. From here, think about which location it's most likely to be in based on how magic squares are calculated and work from there.

Can you reactivate this 4x4 magic square?

We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic:

Objective

Your objective is simple, rearrange the square so that it becomes a valid 4x4 magic square once more:

How to Play

To rearrange the tiles, you'll need to swap them, one by one into their correct positions. For example, the $8$ tile can be swapped with the $1$ tile to effectively place the $1$ tile in a correct position:

However, be very careful on which tiles you swap as there are two important rules to swapping tiles:

1. Each tile can only be swapped the number of times its face represents.
2. 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 $4$ tile:

Two things happen here; the $4$ tile now has 3 moves remaining, as does the $8$ tile. Now, assume you want to swap the $8$ tile with the $6$ tile; in this scenario you can't because $8$ doesn't have 6 moves remaining, it only has 3 because you swapped with the $1$ and $4$ tiles already.

Movement Restrictions

Tiles can be swapped if they are adjacent to each other. Reactivating magic squares is a much more tedious process than deactivating them; as such, outside tiles are not considered adjacent. Diagonal movements are not allowed. As an example, the $4$ tile can be swapped with the $6$, $1$, $3$ and $13$ tiles initially, but no others:

_{Yes, I've created an interactive version of this puzzle. It will be available to the public (linked here) after this puzzle has an accepted answer.}

Clarifications

Does it have to become the magic square you showed? Or is any 4x4 magic square acceptable?

Any valid magic square is acceptable, though answers that don’t use the provided square should explain why they used a different square.

Suppose we're in a position where $8_3$ is next to $4_4$. Is it true to say that "both have moves remaining so they can be swapped" (which would result in all of 8's moves being used and possibly a debt/negative balance afterwards) or "$8_3$ cannot afford to pay the extra penalty, so cannot move at all"?

$8_3$ cannot afford to pay the extra penalty, so you cannot move at all.

Hints

The initial configuration should not be able to be rearranged into the provided valid magic square. This is due to the second row in particular. Instead, you'll need to determine if a new magic square can accommodate the initial configuration, based on known limitations. For example, the $1$ tile only gets 1 move, so it can only be in 1 of 4 positions in the completed grid. From here, think about which location it's most likely to be in based on how magic squares are calculated and work from there.

The question is phrased carefully.

Can you reactivate this 4x4 magic square?

We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic:

Objective

Your objective is simple, rearrange the square so that it becomes a valid 4x4 magic square once more:

How to Play

To rearrange the tiles, you'll need to swap them, one by one into their correct positions. For example, the $8$ tile can be swapped with the $1$ tile to effectively place the $1$ tile in a correct position:

However, be very careful on which tiles you swap as there are two important rules to swapping tiles:

1. Each tile can only be swapped the number of times its face represents.
2. 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 $4$ tile:

Two things happen here; the $4$ tile now has 3 moves remaining, and the $8$ tile now has 3 moves remaining.

Movement Restrictions

Tiles can be swapped if they are adjacent to each other. Reactivating magic squares is a much more tedious process than deactivating them; as such, outside tiles are not considered adjacent. Diagonal movements are not allowed. As an example, the $4$ tile can be swapped with the $6$, $1$, $3$ and $13$ tiles initially, but no others:

_{Yes, I've created an interactive version of this puzzle. It will be available to the public (linked here) after this puzzle has an accepted answer.}

Can you reactivate this 4x4 magic square?

We've already removed the magic from a 3x3 magic square. Recently, one of our 4x4 magic squares was scrambled in an earthquake and I need your help to reactivate it's magic:

Objective

Your objective is simple, rearrange the square so that it becomes a valid 4x4 magic square once more:

How to Play

To rearrange the tiles, you'll need to swap them, one by one into their correct positions. For example, the $8$ tile can be swapped with the $1$ tile to effectively place the $1$ tile in a correct position:

However, be very careful on which tiles you swap as there are two important rules to swapping tiles:

1. Each tile can only be swapped the number of times its face represents.
2. 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 $4$ tile:

Two things happen here; the $4$ tile now has 3 moves remaining, as does the $8$ tile. Now, assume you want to swap the $8$ tile with the $6$ tile; in this scenario you can't because $8$ doesn't have 6 moves remaining, it only has 3 because you swapped with the $1$ and $4$ tiles already.

Movement Restrictions

Tiles can be swapped if they are adjacent to each other. Reactivating magic squares is a much more tedious process than deactivating them; as such, outside tiles are not considered adjacent. Diagonal movements are not allowed. As an example, the $4$ tile can be swapped with the $6$, $1$, $3$ and $13$ tiles initially, but no others:

_{Yes, I've created an interactive version of this puzzle. It will be available to the public (linked here) after this puzzle has an accepted answer.}

Clarifications

Does it have to become the magic square you showed? Or is any 4x4 magic square acceptable?

Any valid magic square is acceptable, though answers that don’t use the provided square should explain why they used a different square.

Suppose we're in a position where $8_3$ is next to $4_4$. Is it true to say that "both have moves remaining so they can be swapped" (which would result in all of 8's moves being used and possibly a debt/negative balance afterwards) or "$8_3$ cannot afford to pay the extra penalty, so cannot move at all"?

$8_3$ cannot afford to pay the extra penalty, so you cannot move at all.

Hints

The initial configuration should not be able to be rearranged into the provided valid magic square. This is due to the second row in particular. Instead, you'll need to determine if a new magic square can accommodate the initial configuration, based on known limitations. For example, the $1$ tile only gets 1 move, so it can only be in 1 of 4 positions in the completed grid. From here, think about which location it's most likely to be in based on how magic squares are calculated and work from there.

Can you reactivate this 4x4 magic square?