 So, what we've done so far is set up a grid, right, a 10x10 grid, and we used sort of Pythagorean tripless simple trigonometry to set up a square grid, right, where we had a horizontal baseline and we set up a 90 degree angle going vertically, and we were able to connect everything up and do vertical and horizontal and have a nice little 10x10 grid, right? And what we did with this grid is we learned our multiplication table, the 10x10 multiplication table, where we laid down the numbers 1 to 10 down here and 1 to 10 up there, and, you know, we filled in the squares here, right, and we figured out what our 10x10 multiplication table is, and that's something really important that you have to learn, right, you have to know your multiplication table before you progress anywhere in mathematics, right? It's basically the first step you need to do to be able to learn math, even before you learn the concept of real numbers and all the subcategories, right, you have to learn multiplication, okay? Now, since we have the grid up, I figured what I was going to do is I was going to show you sort of a math puzzle game that I learned a few years ago from a student that I had, right? And it's a nice little game, and, you know, after my student showed it to me, I ended up playing it for a few months, and it was really fun to do on pen and paper, and it was really meditative, right, it was very chill, I would just sit there sometimes when I just wanted to relax and do this little puzzle game and see how far I could get. And just to give you the details of it, my student, he was originally from Turkey and he said that as far as he knew the game came from Turkey because a lot of his friends played it, and I've never found out the name for this game, so I just keep on calling it a 10 by 10 math puzzle game. And just so you know, it's not, there isn't too much mathematics in it, but one part of math is, the huge part of mathematics is pattern recognition, and I sort of refer to this as a pattern recognition game, because what it is, it's just using numbers sequentially from one, you know, consecutively from one to a hundred to fill in every one of these squares, right, to populate every one of these squares, and the purpose of the game is you start out with the number one, and consecutively you move up, right, so you start out with one, and the next number is two, and the next number is three, and you start putting the numbers in these squares based on two movement types, okay, and we'll go over that, and just to let you know, it's, for me, I played it for a few months after my student showed it to me, and the best I ever got to was to the number 99, that means I was able to fill in every square except for one, and my student told me that he would, he was playing this game for about three years or so, right, and he was only able to complete it once, get to the number 100 once, and it was recently that he did it, that's why it was really exciting, was trying it again, and I saw him doing it, and he showed me how he did it, and he showed me, he actually gave me his solution, and I did do a little write-up on the instructions for this game a few years ago, and I provided that solution in that write-up, and I also provided the solution that I had, that I got to the my best outcome, I guess, which was to the number 99, and just for those of you who are into programming or want to pursue this game a little bit further, a few years ago, when I did write that article explaining what this game was like, and all the rules and whatnot, or the two rules, very simple rules that we'll go over, I got a couple of messages, a couple of comments were posted on that write-up mentioning that people have, you know, they wrote programs to be able to get solutions, so one person, they wrote a program to generate solutions for this, and another person wrote a quick program that you can run on your computer where you don't have to do it with pencil and paper, what you can do it is run this program, and as far as I know the program works fine, because I tried it when he first wrote it and sent me the link to the code and the program itself, and the link is provided in that write-up, but I did try it and it worked fine, and what it does is you run it and it pops up 10x10 grid, and what you can do is just click on the different squares and the numbers pop up, what you're putting in there, the consecutive numbers pop up, and it only allows you to put numbers where the rules specify, right? So if you feel like playing it on the computer, you can do that as well, okay? So that's the little background history on this game, as for the rules of this game, the rules are really simple, the name of the game is, you're going to start with number one, okay? So what we're going to do is we're going to put number one somewhere, right, somewhere in one of these squares, and then we consecutively move up, right? So the next number we have to put down is the number two, but there's restrictions are where you can put down number two, there's movement types, right? So let's put down number one right now, so let's say we're going to put number one towards the center, okay? Now the movement types, there's basically two different movement types you have, if you're going vertical or horizontal, the next number you put down has to be three squares away from this, okay? That means there has to be a two square gap between whatever number you're on and the next number that you're going to be putting down, right? Which has to be consecutive in order, right? So after number one is the number two, right? So we can put number two either one, two, three here, one, two, three here, one, two, three here, or one, two, three here, right? That's the vertical and horizontal movements and they have the same role associated with them, right? Same movement type, right? So we can go one, two, three here, one, two, three here, all right? So the next number is two, I should put that down, two, two, I can go one, two, three here and I can go one, two, three here. That's your vertical and horizontal movement types. The next movement type we have is diagonal and you have to be at 45 degrees so you have to go perfectly diagonal, right? The next movement type you're going diagonal is you can go two units away. So there's only one square gap between your number and the next number, right? So the number two I could place here, I could place here, I could place here, or I could place here, all right? So the next number I can go one, two, one, two, one, two, one, two. Those are the movement types that we have and you know obviously we're not going to put all of these to populate all these fields, all these squares as two, right? We have to decide on one. Now what we're going to do, let's pick, let's go diagonal, let's go straight down to this one, okay? So I'm going to keep this one, I'm going to get rid of the rest. I'm going to consider that to be my movement. Now the next number we have to put down is the number three, right? And the same rules apply. Now we can't go up, right? Because once a field, once a square is occupied, it can't be reoccupied, right? So this one is taken, we can't go there. We can go one, two, we can put a three there, we can go one, two, three, right? We can put a three there. We can't go down here because we go off grid, we can't go off grid, we have to be on the grid, right? We can't go down because that takes us off grid, we can't go that way because that's off grid. We can go this way, so we have, oh, and we can go this way. So we have four choices for our next position, right? We can go one, two, three, we can go here, we can go here, we can go here or we can go here. What I'm going to do, I'm going to go diagonally here. So my number three is going to go here. So I went here, here. Now the next number up is the number four. It's as simple as this. You just consecutively move up. So the number four, I can go here, I can go here, I can go here, I can go here, I can't go there because it's already occupied. I can go here or I can go here. So there's only two spots which I can't go to. I can't go to this one and I can't go to this one because that's going to be off grid. What I'm going to do is I'm going to go right onto the edge because when I was playing this game what I used to do is try to get the outside first and spiral in. Now I'm not sure if that's the best strategy to use or not. Maybe the best strategy is to work from the inside out and I believe I tried that as well a lot but I started sticking with starting on the outside and spiraling in and that got me to the number 99. So what I'm going to do is I'm going to go down here. So this is going to be my next position, number four. Now number five, I can go here, I can't go there, that's taken. I can go here or I can go here. Now what I'm going to do, I'm going to go here, go diagonally across to this guy. So this is going to be my number five. Now just for fun, since we haven't, I haven't done this for a while, let's continue this to see how far we're going to get but that's basically the movement types that we have. So on the write up that I did I provided 10x10 grid paper that you can print off or you can just grab graph paper if you want to do it or run the module, run the program that a user, someone had commented and provided and the link is still up. Now keep in mind with the solution, the one solution that I got from my students, if you get one solution it also means because there's symmetry within this you also have I believe seven other solutions because there's mere symmetry and there's rotational symmetry. So keep that in mind as soon as you have one that means you have seven more because you can rotate them or do mirrors, do symmetry, there's axis of symmetry in these things. But all we're concerned about right now is to get one solution. I've never done it, I doubt it if I'm going to be able to do it right now but who knows maybe it's the luck of the draw. So what we're going to do is from here I'm going to go all the way around so three squares up two unit gap so this is the number six. Okay I'm going to go one two three this is the number seven. Now I can't go here on the top row right I have to go here so I'm going to go you know what the other choice is I can go down this way oops I can go to this one and then come back and then go back up again and then do rotation and keep on filling this guys up right so I would fill all this up but then I couldn't do all the way around again. Okay I hope you see that there's a lot of different strategies you can use for this and I can't remember if my student had told me to use a specific type of strategy or not he played it for three years and he was only able to get one solution and he mentioned that a lot of his friends in Turkey were playing this game and very few of them were able to get a solution okay so this was number seven so I'm going to go to number eight and I'm going to keep on going across one two three this is number nine one two three this is going to be number ten now I have my choices I could come here or I could go there there's only two choices left for this one right oh that side is gone that side is gone I can't go diagonal here here or here right and that one I can't go anymore because I already populated that one so I'm going to go down to here okay this is going to be 11 one two three this is going to be 12 I'm going to come diagonally this is going to be 13 I'm going to come across 14 one two three I'm going to come here 15 now keep in mind you don't necessarily have to use numbers right you could just use spots you could use x's right or colors right different you know pick a color and just start filling in the squares the problem with that though is if you take your eyes off the grid you won't know where you are right with this the numbering system we know exactly where our last movement was right we won't accidentally start from this one and start going off right if we lose our location right so that's the bonus of using numbers right so we're at number 15 now I can go up or I can go diagonal this way right I'm going to keep on going up I'm going to use horizontal and vertical movements for now 16 1 2 3 17 1 2 3 18 1 2 3 19 1 2 3 20 now what I'm going to do instead of coming down I'm going to go diagonal because I want to work on the outside first right so I'm going to go diagonal this is going to be 21 and I'm going to come down 1 2 3 22 1 2 3 23 now I can't come down here but I can go across right so 24 1 2 3 25 1 2 3 26 all right 1 2 3 27 1 2 3 28 1 2 right I'm going to go diagonal hit this one up okay so that's going to be 29 1 2 3 30 1 2 3 31 now you should have noticed something now when I get up to here if you notice this guy the next movement would be here the next movement would be here right so and the next movement would be here so as soon as I start doing this one thing I've noticed is the pattern is obviously I think it's sort of a given that once you have get close to the end the only movements left will just fill up everything that's left right you can jump from one to the other so it gets it done really quickly so where are we we were at 31 okay now I'm going to come down 32 finish one one stack let's go 32 1 2 3 33 1 2 3 34 1 2 3 35 1 2 3 can't do that's taken right so what I could do is come here but I can't get back to that one if I come here I can go diagonal again so what I'm trying to do is get to this outside surround right because if I get there all the sides are done right so we're here right now I could go here and come down and now I'll get to the square and that way I can move my way around right so let's do that one right so I'm 35 I can go 36 here now I can go diagonally 37 down here so 37 and now I should be able to do all these jumps right so let's do it 37 38 now one strategy could be to keep all these jumps for the end right that way if you can take care of all the middle guys all you have to do is get to one of these squares and you're done right but let's do it this way for now that's something you can try yourself if you like this might get me addicted to start doing it again I played it for a few months uh barely regularly because it was a lot of fun 43 45 so we got 48 done we're almost done almost half the squares right because 50 is half the squares but it seems like there's a lot of squares left that's because on the outside it takes more numbers to cover right so this thing what happens is initially it's a lot of choices and slowly your choices decrease decrease decrease and towards the end you really have to think about you know where are you going to go so 48 I'm going to go to 49 50 and I'm going to keep the same strategy doing the outside first or trying to do as much of the outside as possible because that's where most of my squares are right 51 52 I can't go diagonal I'm going to come down before 123 down here 55 let's go across 123 56 let's see what can we do okay what I'm going to do I'm going to come across here that way I can get to here and then zap these guys so 56 57 and then I'm going to come down 58 this might not be the best strategy you might it might be smart to leave some space on the outside so you can go in and out right but we're going to try this for now 59 60 61 62 I can't go sideways so 63 what I could do is come here yeah let's go straight down here for now 63 so my choice here is gone I could go diagonal here I could go diagonal here I could come straight here which way to go if I go diagonal here I'll go here here here I can zap those guys inside so let's do that on the outside right so 63 I'm going to go 64 I'm going to go one two three 65 I'm going to go one two three 66 one two three 67 68 right and hit that one that one and that one as well 68 69 70 71 now 72 I can't put there I only have one choice for 72 right there right if I go 72 73 74 75 76 and then I can come out of that right okay let's do that so 71 72 I can go diagonally 73 I can come back here 74 I can come down 75 76 we have one choice left for 77 now I have to go here right one two 77 now this is where your choices are totally becoming less and less right so 77 two I can go here 78 I can go here 78 or I can go here 78 now here I can go 78 79 80 81 82 and that'll be stuck so that's not good let's see 77 78 79 80 81 82 83 I think so so let's do that one 78 79 80 80 81 82 and go down to 83 I think I'm putting myself into a corner I think I'm going to be stuck on the next move now the best I've ever done is 99 this isn't even close towards the end once I got the hang of this I was going into the mid 1990s or mid 90s right so what do we have we had 83 84 and I would be stuck if I do 84 84 that works and then 85 that works so let's do that so 84 85 all right I could do 85 over here 86 the same deal 87 88 okay let's see 84 85 actually let's do this 84 I could come here 85 86 87 88 we could do that too let's do this one 85 86 right 86 I can go up 87 I can go sideways 85 86 87 88 I can go 89 that's my only choice for me all right I got nothing else 89 I got 90 is that it oh I can go here oh I can do this one so 90 that's better one two three 90 I can go 91 91 that's good that gets us closer 91 I could go 92 93 I would be stuck I can go 92 93 94 oh that's not bad 91 92 93 94 I can go up there 95 that's my only choice for 95 and I think I got one more choice left that's it and 96 96 could be I've done something else I don't think so 95 if I could get to this one or that one I could have filled both of those and we could have got 98 but 96 96 is not bad right I didn't try this for a while so 96 so four missing right four we've got four gaps here one two three four four minus 100 is 96 and you know I guess that's in the range I used to be able to get and I think if there was a point system associated with this game you would have to say that he would sort of have an exponential uh sort of a point system where the closer you got to 100 the points would be doubled or one and a half times right because 97 if I got to 96 let's say that was worth 10 points if you get to 97 that should be worth not just 11 points but a lot more so it should be worth like 15 points or 20 points 98 maybe a lot more than that right I don't know if you want to use logarithmic scale that's a little too high but if you do do this with a point system I think there should be some kind of exponential growth associated with this with the points that you do get okay and this is the game this is a 10 by 10 math puzzle game that my students showed me and I call this a pattern recognition game because it is really a pattern recognition game right um it's fun to do and it's pretty it's interesting okay and it's puts your mind in the neutral and you can enjoy it and uh and uh just shows it for a bit um it's sort of like that Japanese game I think it's Japanese Sudoku uh where you you know you know the columns and the rows add up to nine or different variations of that right uh but this one doesn't require any adding at all uh it's just sequentially consecutively moving up knowing your position your last position and having two movement types to put the next number down okay I hope you enjoy it learn how to set up a grid learn your multiplication table and learn a nice little game one a 10 by 10 grid I'll see you guys in the next video bye for now learn that let's take down this grid