YouTube user singingbanana, whose videos will interest Grey Matters readers, has just posted some interesting videos concerning the humble 15 puzzle.
If you'd like to follow along with these videos, checkout the cut-the-knot's Fifteen puzzle page (Java required) to try the puzzle out for yourself.
To learn the basics of solving 15 puzzles, see Jaap's 15 puzzle page.
The first video concern's Sam Loyd's classic 15/14 version of the puzzle. If you're using the cut-the-knot version to which I linked above, you can use the Cheat button to start from the 15/14 version to try this challenge out:
As you may have guessed by the ease with which singingbanana offers the $1,000 reward, getting to the standard solution from a position starting with the 15 and 14 switched is impossible.
The question is, why is it impossible? That's answered clearly in the follow-up video, where three challenges using the 15/14 version are added:
Can you meet these challenges? Try them out for yourself before proceeding any further.
Some of you may remember that I taught an approach to a 15 puzzle magic square a few years back, which I later demonstrated on video. However, the one I teach requires that you start from a standard 15 puzzle. If you start from the 15/14 version, as in the final challenge in the above video, you can't do it exactly as I teach.
However, if you understand the principle taught in the video, you should see how it's possible to adapt my magic square approach. Again, try it out for yourself before proceeding any further.
Here's my answer to all three challenges, and you'll see how I adapted the magic square for the 15/14 puzzle:
How did you do?