#### molarmanful

##### Member
Hey guys,
I feel like 15 puzzle deserves a thread, even though it's not an official WCA event or twisty puzzle. I'm sure that a lot of people could benefit from the help and discussions in this thread. If this is in the wrong forum category, feel free to move it (if you're a moderator).

That being said, I'll outline some basic steps and tips for solving the 15 puzzle with LBL (if there are other methods, please describe them in a reply):
[HR][/HR]1. First row (FR):
Code:
1  2  3  4
x  x  x  x
x  x  x  x
x  x  x  x
Generally, you solve as 1-2>3-4, but if you want to get faster, try solving 3-4>1-2, 2-3>1-4, etc. depending on the situation. You can also solve 1,5,9,13 as a 'row.'
If possible, try to solve some of the second row pieces while finishing FR. For example:
Code:
2  x  3  4
x  x  x  x
1  x  x  x
5  x  x  x
----------
easily becomes
----------
1  2  3  4
5  x  x  x
x  x  x  x
x  x  x  x
2. Second row (F2R):
Code:
1  2  3  4
5  6  7  8
x  x  x  x
x  x  x  x
Solve the second row like you solved FR. However, you might want to try fringing, or solving a column while doing the second row. After fringing, you'll end up with this:
Code:
1   2  3  4
5   6  7  8
9   x  x  x
13  x  x  x
3. L8P (or L6P if you fringed):
Code:
1   2   3   4
5   6   7   8
9   10  11  12
13  14  15  0
Solve 9 and 13 first if you haven't already. Then proceed in one of two ways:
a. Solve 10-14>11-12-15. Conventional way, relatively easy L3P, okay chance of L3P skip.
b. Solve 11-12>10-14-15. Only use this if 11 and 12 are easy to place (i.e.: not flipped the wrong way). Super easy L3P, high chance of L3P skip.

[HR][/HR]You should also try out SlidySim, a nice 15 puzzle simulator that also contains slidy puzzles of other sizes.

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#### cashis

##### Member
Cool guide. Thanks for making this thread.

#### 4Chan

If 15 Puzzle starts gaining momentum, and quality speedsolvable 15 puzzles (or larger) become available, I will be so happy.

Please keep this up! 15 Puzzles are cool!

#### TDM

##### Member
You should probably add ben's sim to the OP, since it's what most people use.

just recorded a 15 puzzle Ao5, uploading now, will post here when it's done
E:

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#### qqwref

##### Member
I'm not sure this really needs a home thread other than ben's sim thread, but okay. Here's some useful solving info.

The standard speed method for smaller puzzles (like 15 puzzle) is fringe. Basically the puzzle gets divided up like this:
Code:
A A A A
A B B B
A B C C
A B C
You would solve the A pieces first, then the B pieces, then the C pieces. Inside each fringe, you can either do the row part and then the column part, or the column part and then the row part, or both at once (if you see a way to do that). More efficient solvers use a lot of clever tricks to solve fringes, which you can learn from watching Ben's videos or optimal-fringe solves.

On smaller puzzles you can get away with moving pieces over one or two at a time, but on medium size puzzles (such as 99 puzzle) you will want to move trains of a few pieces up or left at once - that is, you might find 3-4 pieces from the first fringe's row, then put them in a column and move them all up in a single looping motion. I usually try to find all the pieces

On very big puzzles, fringe does work, but it becomes hard to tell the individual fringes apart, since there are so many colors. The best method seems to involve the grids color scheme, with a secondary scheme. Essentially the puzzle is grouped like this:
Code:
A A A B B B ...
A A A B B B ...
A A A B B B ...
C C C D D D ...
...
The squares A, B, C, D, ... can be any size but are commonly 1/4 or 1/5 of the main puzzle's size (so there will be 16 or 25 of them). Each of these squares has its own color, and then within a square, the secondary scheme lets you tell pieces apart so you can do a fringe or LBL solve. As for the actual method, you would bring all of the pieces of the first row of grids up to those locations, making a big rectangle; then, inside that row, you would bring all of the pieces of the first square left; then you would solve the first square. After that, you keep sorting squares until you finish the row, and then you do the entire thing again for the other rows of squares.

Also, people should learn mouse Keyboard+macro > mouse > keyboard in terms of speed for big puzzles, but I and some others don't believe macros are fair comparison. You can do many moves per keystroke and get bursts of 100+ tps easily - it breaks the rule that an NxN puzzle should take (constant * N^3) inputs, and gives the grid method an artificial advantage due to working really nicely with spamming whole-row rotations (like L50 U R50 D ...).

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#### TDM

##### Member
Edited the previous post. Check the link.
What's the bit of plastic sticking out of the 12 piece? Do all the pieces have that? That doesn't look like it's really doing much.

#### cashis

##### Member
What's the bit of plastic sticking out of the 12 piece? Do all the pieces have that? That doesn't look like it's really doing much.
I'm pretty sure that's what keeps the pieces from falling out...it interlocks with grooves on the other pieces

#### cashis

##### Member
Oh, of course.
But then... how did you get the pieces out to mod them?
I guess just rip it out like a regular cube.

#### molarmanful

##### Member
Oh, of course.
But then... how did you get the pieces out to mod them?
Yeah, there are grooves to keep the pieces from falling out when overturned. I basically pried out the 12 and 15 pieces with a screwdriver (didn't break them, luckily) and everything was super-easy to disassemble after that. For reassembly, I broke off a bit of the 12 piece's "torpedo" so that the the torpedo could actually fit through the florian mod holes.

#### The Professor Cubers

##### Member
It seems as though the 15 puzzle hasn't been very popular over the past few years but I recently got into it myself. I think it would a cool event to have competitions for but I don't know how big the audience is for it. If anyone would be interested in trying to hold a competition please reply so we can make that happen.

#### Mech

##### Member
Hello, can anyone solve this? It's basically 15-puzzle but with numbers 1-8. The right one is how the left should look like in 62 moves

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