Solution to Tiger sliding-puzzle game

[commonpeople]

Here's a way I worked out for solving the Tiger widget 4X4 sliding puzzle. I don't claim it's the best solution but it always works. Let me know if you have any improvements.

Notation

label the squares

A1 A2 A3 A4
B1 B2 B3 B4
C1 C2 C3 C4
D1 D2 D3 D4

The idea is to split the puzzle up into several smaller mini puzzles. Note that when the puzzle is finished D4 must be the blank square, so it seems like a good idea to start completing the puzzle away from D4 and work inwards so that the last bit to be solved is the area around D4.

In each step of the following 'Solve' means A) put the right tiles in the indicated boxes. This can be done in any order, whichever is most convenient. B) After all tiles are in the named boxes then leave them in place... they never need be moved for the rest of the solution. (Of course sometimes you may want to move them if you see a shortcut- but the point is that they don't have to be moved.)

Here are my steps:

1) Solve D1, C1, B1, A1 (moderate)
2) Solve A2 (easy)
2) Solve A3 A4 (moderate/tricky)
3) Solve D2 (Easy)
4) Solve C2, B2 (moderate)
5) Solve B3, B4, C3, C4, D3, D4 (tricky)

The last step involves swapping around the last 6 squares (including the blank) in a 3X2 rectangle on the bottom right. I don't have a proof, but it seems that no matter which way the pieces are arranged the last 6 can always be swapped around to finish the puzzle.

I suspect that steps 3)-4) could be replaced with the following without any obvious change in difficulty

3b) Solve B2
4b) Solve C2, D2

Of course, none of this is a complete answer- I haven't specified how to carry out each 'mini-puzzle'. For instance steps 2 and 5 can occasionally be tricky. It would be nice to investigate better how to complete these steps with less guess-work.

Let me know if anyone finds a more efficient sequence. BTW... yes I know that we can probably find the ultimate answer on the internet somewhere, but let's have a little fun and think for ourselves for at least a few days.

Christian

 

[AppleMatt]

Woah that's determination. Impressive, because you deducing this will have gained a lot more benefit than anyone using it.

I've just started getting into Suduku, but it usually ends up annoying me before I solve it. I prefer 3D puzzles that I can touch and manipulate.

AppleMatt

 

[Bozola]

I always did it this way

A1,A2,A3,A4 (easy)
B1,B2,B3,B4 (easy)

C1,C2,C3,C4,D1,D2,D3,D4 (tricky)

 

[puckhead193]

why couldn't they just have the jig-saw puzzle with the map from back in the day

 

[commonpeople]

I always did it this way

A1,A2,A3,A4 (easy)
B1,B2,B3,B4 (easy)

C1,C2,C3,C4,D1,D2,D3,D4 (tricky)

Yes, that seems to work quite nicely as well. The last step is by far the hardest- do you split that into the following?

Solve C1,D1
Solve C2,C3,C4,D2,D3,D4

Or do you find it easier to not 'fix' any pieces in the last part of the solution?

 

[Applespider]

I've just started getting into Suduku, but it usually ends up annoying me before I solve it.

I love Su Doku! Practice on the Times 'mild' ones (Monday, Tuesday in the paper, Tues/Wed online) to start with before building up to fiendish ones. They're usually solvable by simple observation of the column/row rule rather than having to get into the 'box' logic.

 

[iMeowbot]

why couldn't they just have the jig-saw puzzle with the map from back in the day

The slide puzzle is from back in the day The very first Macs had it.

 

[commonpeople]

By the way- isn't there a way to change the picture in the sliding puzzle. I haven't been able to find it.

Christian

 

[HexMonkey]

By the way- isn't there a way to change the picture in the sliding puzzle. I haven't been able to find it.

Start dragging an image file in Finder, activate Dashboard, then drag the file on to a Tile Game widget.

 

[feakbeak]

Start dragging an image file in Finder, activate Dashboard, then drag the file on to a Tile Game widget.

Cool, I was wondering how to do that. Yet another way to revitalize my pr0n collection!

 

[commonpeople]

Improved solution

Here's a way I worked out for solving the Tiger widget 4X4 sliding puzzle. I don't claim it's the best solution but it always works. Let me know if you have any improvements.

Notation

label the squares

A1 A2 A3 A4
B1 B2 B3 B4
C1 C2 C3 C4
D1 D2 D3 D4

The idea is to split the puzzle up into several smaller mini puzzles. Note that when the puzzle is finished D4 must be the blank square, so it seems like a good idea to start completing the puzzle away from D4 and work inwards so that the last bit to be solved is the area around D4.

In each step of the following 'Solve' means A) put the right tiles in the indicated boxes. This can be done in any order, whichever is most convenient. B) After all tiles are in the named boxes then leave them in place... they never need be moved for the rest of the solution. (Of course sometimes you may want to move them if you see a shortcut- but the point is that they don't have to be moved.)

Here are my steps:

1) Solve D1, C1, B1, A1 (moderate)
2) Solve A2 (easy)
2) Solve A3 A4 (moderate/tricky)
3) Solve D2 (Easy)
4) Solve C2, B2 (moderate)
5) Solve B3, B4, C3, C4, D3, D4 (tricky)

The last step involves swapping around the last 6 squares (including the blank) in a 3X2 rectangle on the bottom right. I don't have a proof, but it seems that no matter which way the pieces are arranged the last 6 can always be swapped around to finish the puzzle.

I suspect that steps 3)-4) could be replaced with the following without any obvious change in difficulty

3b) Solve B2
4b) Solve C2, D2

Of course, none of this is a complete answer- I haven't specified how to carry out each 'mini-puzzle'. For instance steps 2 and 5 can occasionally be tricky. It would be nice to investigate better how to complete these steps with less guess-work.

Let me know if anyone finds a more efficient sequence. BTW... yes I know that we can probably find the ultimate answer on the internet somewhere, but let's have a little fun and think for ourselves for at least a few days.

Christian

OK, I've been playing around with the puzzle a little bit more- and I now think that there's really no particularly best order in which to solve the initial steps- It can be pretty much done in any order you wish. However, it all comes down to the 'end-game'. You need to finish up with a block of 3X2 (including blank) on the bottom right like so:

T T T T
T T * *
T T * *
T T * *
(T indicates tiles already solved; * indicates tiles to be solved including blank)

I've then found that the easiest way to solve from here is to 'Solve' the top 2 T's (which are then fixed) leading to 4 pieces (including blank) which can always be swapped around to complete the puzzle.

So- a complete solution might look like this (F means tiles 'fixed' in place)

Step 1
T * * *
T * * *
T * * *
T * * *

Step 2
F T * *
F T * *
F T * *
F T * *

Step 3
F F T T
F F * *
F F * *
F F * *

Step 4
F F F F
F F T T
F F * *
F F * *

Step 5
F F F F
F F F F
F F T T
F F T T

Once again- at each step the tiles to be solved can be done in any order and then they can remain fixed in place for the rest of the solution (i.e. they need never be moved again to complete the puzzle).

Let me know if you have any further thoughts.
Christian

(I edited this post because I messed up some of the notation!)