Hi everyone, it's Jerry. The knight's tour
is a challenge for those who are interested
in mathematics. It involves moving the knight
about on the chessboard so that all squares
are covered exactly once. And you don't need
to know how to play chess in order to do it,
but rather just know how the knight moves
and by following just a few simple rules you'll
be able to do this and maybe challenge a friend,
math teacher, or should you be a math teacher
watching this, challenge your classroom. So
that's what I'm going to show you how to do
in this video right now. Okay so it's important
to visualize the board broken up into four
quadrants four groups of sixteen squares,
and within each of these quadrants we have
four systems to be familiar with. Now what
am I talking about? I'm talking about a left
diamond system. It's of a diamond shape and
it's pointing towards the upper left in each
of these four quadrants. Okay, this is a left
diamond system. We also have a right diamond
system to be familiar with. The only difference
is that it's pointing towards the upper right
in each of these four quadrants. And an important
visual cue is to know that when we combine
the left diamond system and the right diamond
system, that within each quadrant all four
central squares will be covered
and all four corner squares will be covered.
Okay so just an important little tip I believe
for when you try to do this on your own. The
only other systems we have yet to touch, these
still highlighted are the left and the right
diamond ones, the only ones we have yet to
cover are these b8 c8 a7 a6 these edge squares
within each quadrant. And let me identify
those last two systems. We have what we'll
call a left square system. We had both b8
and c8 to cover, so let's call this a left
square system since we're starting with this
b8 square. And we would move about like so
in this square shape along the edge within
each quadrant. And lastly a right square system,
moving about like so in again each quadrant.
So just a very quick recap we have a left
diamond system, a right diamond system, a
left square system,
and a right square system. So, putting this
all together let's get going. Let's randomly
place the knight. He's starting out on e7,
now the very first question to ask of yourself
is "in what system is this knight located?".
If you guessed he is in a right square system,
you are correct. Okay, so the objective at
this point is to complete all of these highlighted
squares, to complete all of the right square
system. And we do that by completing all four
squares of this quadrant right here for starters,
and then we jump into a new quadrant. So whatever
quadrant he starts out in we complete all
four squares within that quadrant and then
jump into a new quadrant. And what we'll see
along the way is that we have to make some
important decisions. There are times where
we could just not go wrong, but they're certainly
times where if we don't do a little bit of
calculation we can mess this up. But we're
not going to do that we're not going to mess
up here. So we'll start out with
g8 h6 and then this f5 square. We've completed
these four, now it's time to jump into a new
quadrant. I can go into this one here, I can
also go into this one here on e3. Let's go
to this e3 square and now it's an important
decision because if I make use of f1, that
means I end up getting stranded on this g4
square and, I can't get into, I'm stranded
because I can't get into one of those last
two remaining quadrants. So knowing this we
need to make use of first g4 h2 f1 and then
I get into that new one. Similarly, if I go
to this square I end up getting stuck on b1.
That's something to avoid. I don't have a
decision here, and it's not going to matter
at this point what direction you go, but a
rule of thumb I like to follow is just to
try and keep the knight as central as possible,
and with that last move I have completed the
right square system. So, we've completed a
right square system. Let's now complete a
diamond system. In fact, we could only jump
into now a diamond system. And since we did
the right square system, lets now complete
the right diamond system. So showing what
those are highlighted let's go forward with
this d4 square and it doesn't really matter
in what direction you go in at this point.
And now it does matter, because if we make
use of c6 we end up getting stuck here. So
again a little bit of calculation needed.
We don't want to go here because we end up
getting stuck on f7, so let's make use of
f7 first. And I'm just going to stay as central
as possible ending up here on this f3 square.
We have just finished the right diamond system.
So the last two to cover, we now have a left
square system to complete. So let me do that
right now. And as we also have another decision
at this point. We don't want to go to this
square first, we'd get stuck on a2. So let's
make use of a2 first. And then we jump into
this one. We don't want to get stuck on a6,
so let's go to a6 first. And we don't have
a choice here. And it really is not going
to matter, I'm just again following my rule
of thumb I'm going to try to keep my knight
as possible. So we've completed three systems
so far, we
only have one remaining. Namely, the left
diamond system. So just finishing up completing,
again, all four squares within each quadrant
before you jump into a new quadrant. And we
don't want to get stuck in the corner so let's
make use of that corner square first. And
I don't want to get stuck over here on a4,
so let's make use of a4 first. And you pretty
much just can't go wrong at that point. So
that's the knight's tour. I hope you enjoyed
it. Leave a comment. Let me know what you
think. And if you're able to do this, maybe
you can post a video response and show yourself
doing this. And that's pretty much it. So
again I hope you enjoyed it and that's all
for now. Take care, bye.
