In the quick look for The Tomorrow Children and in the recent podcast, the team complained about the sliding block puzzles, saying how much they hate them and how hard they found them. I figure some people in the GB community might have the same trouble, so as a public service: here's a very simple guide to solving every solvable sliding block puzzle ever:
gkhan's foolproof guide to sliding block puzzles
Solve the first row and first column first, then the second row and second column, etc.
That's the general stragegy. Think about it: if you have a 5x5 puzzle, solving the first row and first column reduces the problem to a 4x4 puzzle. You will never have to touch that row and column again. You then keep doing that, solving smaller and smaller puzzles until you're done.
To solve the first row, line up all numbers in their proper place except the last two
So, in a 5x5 puzzle, put the 1, 2, and 3 blocks in their proper place. You should have no problem doing this, you wont mess up previous positions.
Put the next number in the top right corner, then the next number below it
See how the 1, 2, and 3 blocks are lined up? The next number (4), is put in the top right corner, and the number after that (5) is below it. What is currently in the "4 spot" (a 9 in this example) doesn't matter.
This shouldn't be too difficult. Move the 4 first, then the 5. If you find that they get "tangled up" in each other, move the 5 away a block or two first so you can properly position the 4.
(incidentally, I'm using screenshots from this site for the images)
Now just "rotate in" the remaining two numbers
Move your empty place into the spot where the 4 should end up, then move right and down. Congratulations, you've solved the first row.
Do the same for the first column
Now, move the blocks in the first 3 numbers in the first column to their proper position, then put the last two in the bottom left, similar to how you solved the first line. Notice that the 1, 6, and 11 are in their right spots, and the 16 (the next number) is in the bottom corner and the 21 is right after that.
Then, just "rotate in" the numbers (from this position, by moving down and right), just like you did with the first line.
This "rotate in" trick is the key, here. You'll never have trouble getting the first numbers of a row or a column right, but the last two can get "entangled" up in each other and be put in the wrong order. But if you do this, you'll get it right, every time.
Now you have a 4x4 puzzle. Proceed in the same manner.
Your first column and first row have been set, you should never touch them again. You don't need to. Imagine that the first row and first column are just "gone" or something. Just do the "first line" of this new puzzle (which is the second line of the whole puzzle) in the same way: line up all the numbers except the last two, put them in the corner, and "rotate in".
Solve the column in the same way as before, line up all numbers except the last two, then "rotate in" the last two.
Now you have a 3x3 puzzle
You get the idea. Line up the first number in the first row, then rotate in the next two, do the same for the column
Now you have a 2x2 puzzle
Just rotate clockwise or anti-clockwise enough times, and the puzzle will be solved. Good work, you!
Congratulations! You can now solve every solvable sliding block puzzle ever!
You don't need to follow this guide religiously. If you really want to, you can solve the first two lines before you tackle the columns, for instance. It also wont give you the optimal solution, but you wont get that any way. This way it ALWAYS works out, if the puzzle is solvable at all.
Sliding block puzzles still suck, though
Once you learn this trick, sliding block puzzles goes from incredibly annoying to basically trivial. You can solve every sliding block puzzle like this, and it requires almost no "thinking", it's entirely mechanical. Unlike, say, Sudoku or Picross, no sliding block puzzle will ever be "interesting" or "fun to solve", because you already know the trick to how to do it. Instead, they become incredibly tedious, because you know exactly what you need to do, and now you just have to execute everything, which is incredibly boring.
Game developers: never put sliding block puzzles in your games. Either they're annoyingly hard if you don't know how to solve them, or they're trivial and tedious if you do.