Do you remember the Guarni puzzle we covered in the previous episode?
It was a change in the knight's position.
I wanted to express the knight's movement path like a thread and show the feeling of unraveling a tangled skein of thread.
It was a pity that I couldn't show it in the previous video, but I can finally show it to you.
I wanted to make a video of the thread unraveling and turning into a circular necklace, but I failed due to lack of ability.
Still, I expressed it this way because I thought it would be easier for you to understand if you saw the two together.
To put it more difficult, it turns it into a problem about the topological order of four points located on a closed curve.
As you solve math problems, you change your thinking a lot.
Even when students solve problems that would be easier to see if expressed as a circle,
they forcefully twist the problem like a tangled skein of thread.
Then, if we solve it well like now and make it neatly like a pretty circle, it will be easy.
The circularity that was not visible on the chessboard becomes clearly visible when viewed as movement in a circle.
Then, you can know how to move efficiently and what the minimum number of moves is.
If you all move clockwise one space at a time, you can change the knight's position in 16 times.
This time, one white knight has changed into a red knight.
To change the knight's position, if you look at it as a bead necklace and move in order,
16 times is enough in the same way as before.
Turn it clockwise.
That doesn't work.
Turn it in the opposite direction again.
It doesn't work either.
If you look at it on a chessboard, it may be very difficult, but if you look at it as if it were spinning in a circle,
You can see that no matter how much you turn, it won't work.
It feels similar to Sam Lloyd's '14-15 puzzle'.
This problem can be easily thought of as a problem about the topological order of four points located on a closed curve.
It would be very difficult to just move.
It is a meeting of chess, math puzzles, and mathematics.
The numerical problems I had to solve while teaching students were not fun.
But actually, you can see that the number of cases is a lot of fun when you come across this problem.
Think of the knight's difficult movement path as a bead necklace and change it back into a simple shape.
If you just remember this today, difficult problems will become easier to approach.
We're always talking. “Change in thinking is important. Make it brief.”
So let's take a look at the route.
The original path is not pretty.
If you look closely, you can see that it is circulating in a regular hexagon shape.
However, it is a bit difficult because there are two regular hexagonal paths.
Still, it's much better than the path on the left, right?
Try this yourself and see how it circulates.
It is very helpful to think about what would require the least amount of movement.
thank you
This is a YouTube video link.
https://youtu.be/y3b4YTcQz04?si=TjRIxQLNMeiArIim
