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A Strategy for Beating the 15 Puzzle (Without a Solver)


Fragarach Luin
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So, it appears from all of my Google searches that no solver program exists online for the 15 Puzzle that is compatible with a mobile device. Since I haven't had access to a computer while through-hiking the Appalachian Trail, I was forced to obtain the "Half-Minute Hacker" achievement legitimately, and so I thought it might be nice to write up a short guide here in case there are any others out there who are unable to use the Solver method outlined in the achievement guide. I had never played the 15 Puzzle before, and there may be more optimal solutions out there than the one I figured out, but eventually I was able to complete the puzzle in 27.98 seconds using my strategy. Unfortunately, this isn't a magical solution that will get you the achievement in seconds, rather, it is a strategy that will always solve the puzzle. It's my opinion that most puzzle configurations cannot be solved in 30 seconds, solver or no. Earning the achievement legitimately will require dedicated practice, but not too much (it took me about 2 hours to become fast enough to complete a favorable configuration).

 

Just for reference, it took me 16 minutes to solve the puzzle the first time I attempted it. I earned the achievement on attempt number 130, after previously finishing with a heart-breaking 30.25 seconds 20 attempts earlier. For the last hour or so of attempts, I was consistently able to beat the puzzle in under a minute, but as I said, once you are fast enough, it's all dependent on the puzzle configuration you start with.

 

Anyway, here's the strategy.

 

The object of the puzzle is to move each number into its proper position in the puzzle. A completed puzzle is numbered in sequence, from 1 to 15, horizontally, in descending rows from left to right. Here is a completed puzzle, for reference (and to drive home the reliability of this solution, notice that I casually got a time of 30.71 seconds in the process of obtaining this screenshot):

 

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I always begin with 1, and put each number in its place in order. It's fairly obvious how to move each number in the beginning, but it takes practice before you can quickly and automatically see where a number is and where it should be. That practice is the true key to beating the puzzle quickly, but it doesn't require much explanation, just muscle memory.

 

Now in the process of moving the starting numbers into their positions, you will come to the number 4 and realize that you haven't got the space to get it in the corner without at least disturbing the 3. My strategy is simple, and always repeatable. Keep the 1-2-3 in order, but move the whole lot of them down and around the lower corner. Then circle the 4 around into the corner where it needs to end up. Then move the two inconsequential numbers down and out of the way, and move the 1-2-3 back up and around the opposite corner. Voila! First row done (and don't worry, there are pictures illustrating what I'm talking about).

 

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Notice the 4 is in that group of three numbers in the upper right corner?

 

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Slide the 1-2-3 down and around, keeping their order intact.

 

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Circle that group of 3 numbers containing the 4 until the 4 is in its final spot.

 

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Move the inconsequential number down and slide the 1-2-3 back into place.

 

After this you can do precisely the same with the 5-6-7-8. I will demonstrate once again with pictures below. Try and follow along, the strategy is identical.

 

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Now it gets tricky. This is the part where you will know if you can earn the achievement or not. Begin by moving the 9 into place as usual. At this point, however, if the 10, 11, or 12 end up in the lower left corner, you will need to move the 9 out and actually just work on trading out that 10, 11 or 12 for a 13, 14, or 15 (preferably the 13). In any case, it's easy, but takes time.

 

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Notice how the 10 is in the corner? Not ideal.

You have to forget about the 9 for a second and work on moving that 10 away. And to be safe, make sure that you replace it with a high number. If 11 or 12 get stuck there, you'll just be repeating this step.

 

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Now that the 15 is in the corner, we can solve the third row exactly like the first two.

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Okay, home stretch. The 13, 14, and 15 can't be solved like the rest, because there's no room left to work with. Fortunately, the chances are quite good that you'll end up with the final three numbers in order, but it's not the end of the world if you don't. Once again, the important trick to rely on is keeping your numbers in the correct sequence, even if you have to move the entire sequence. In this case, the best way is to split the 9-10 away from the 11-12, and move the odd one out of the bottom three upwards. For example:

 

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In this case, the 13 and 14 are in order, so the 15 is the odd one out. Because it's on the left side, we want to move the 9-10 down.

 

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From here it's pretty obvious. Move the 15 up, which frees the 13-14 to move over, then move the 11-12 down.

 

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And now get the 15 over, the 9-10 back up, and lastly, drop the 15 into place and move 11-12 back.

 

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Congratulations.

 

One important trick that will shave off seconds is that you can move whole rows of numbers with one tap. If the empty space is on an edge, for example, tapping the number on the opposite side will shift the whole row over.

 

It's important to not let the puzzle stress you out. Most configurations will not afford you the possibility of earning the achievement, but if you let that frustrate you, you will start getting distracted, making mistakes, and ultimately run the risk of missing your chance when it does come up. Not all configurations can be beaten in 30 seconds, but they are all good practice. When I earned the achievement, I had to take the extra step to fix my final row, so it doesn't have to be perfect. Practice and patience really are necessary. I just hope that this guide can give someone the direction and confidence they need to begin practicing. It's truly not that hard; you don't need to be a genius.

Edited by Fragarach Luin
Got the achievement name wrong, go figure.
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