Make A 9x9 Magic Square! Learn The Ancient Chinese Algorithm (Lo Shu Square)

Magic squares are arrangements of numbers where every row, column, and diagonal adds up to the same number. The ancient Chinese developed a geometric method to create 3x3 magic squares. Remarkably, they generalized the method to create a 9x9 magic square which is quite the feat!
The Lo Shu Method From "The Evolution of Mathematics in Ancient China", Frank Swetz, Jan 1979. Appears in "Sherlock Holmes in Babylon." amzn.to/1c2QBSm
Lo Shu Square courtesy Wikipedia
en.wikipedia.org/wiki/File:Lo_...
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[@mattsmith457]

I made a square out of mild/subtle numbers. I call it the Lo Kee square.

[@TSDLoading]

You can also take all these 3x3 squares and put them in ascending order from the right, like single numbers. Then use the Lo Shu method to arrange them like the final state.

[@notoriouswhitemoth]

The Lo Shu square is a very significant symbol in taoism - one of the oldest visual representations of the relationship between yin and yang. Where the odd numbers are highest, yang (the active force) is strongest. Where the even numbers are highest, yin (the receptive force) is strongest. It really isn't about the numbers so much as the relationships among them. For everyone here who found this informative - especially a certain subset, you know who you are - please understand this: YOU JUST LEARNED MATH FROM A RELIGIOUS SYMBOL. Consider that if you ever so much as think that religion encourages ignorance.

[@sutfolsemaj]

+notoriouswhitemoth And most serial killers are quite nice when you talk to them in public.

[@gusriley9785]

@@sutfolsemaj Have you spoken to many?

[@1invag]

But I could just interpret it as positive or negative and set any other potential interpretations aside as speculatary. 😕 Although I've already interpreted it once before declaring interpretation irrelevant lol. Ohh great it's 11.11 pm... Pisses me off haha

[@evilkillerwhale7078]

@MindYourDecisions, there's a neat algorithm we learned in middle school for ANY odd sized magic square. Consider edges wrapped (so going off the top would go to the bottom, and the right would go to the left). Start in the top middle with 1. Go "up right" and end over to the right one column, at the bottom of the square for 2. Continue going "up and right" one square while incrementing until you hit another number. At that point, go down 1 space, increment, and then return to the previous algorithm. When the square's complete, you have a magic square.

[@Anonymous-jo2no]

Demonstrate it please? With 5 x 5.

[@evilkillerwhale7078]

***** imgur.com/gallery/nwPT4 That work?

[@StevenTorrey]

The "magic" behind this is that you are essentially adding up the same number, minus one. The appearance of adding up different numbers is just that, an appearance.

[@KarimLahlou]

This is amazing. Thank you for the video,, keep up.

[@ittesafyeasir3438]

for the 3x3, just start with 1 on the (3,2) square and follow 1. try to go diagonally downwards to the right, if there are no squares there, imagine that the square is a cylinder and thus mive there. for e.g. from (3,2) we shall go to(1,3) 2. If the square already has a number, just go one square to the top. e.g. from (2,1) to (1,1) for the 9x9, make your 9x9 box and fill out the 3x3 square's numbers as shown in tge last part of the video. then for each 3x3 square, follow the above methods but instead of writing the numbers serially, we write (+9) so after 1 we write 10

[@rajendralekhwar4131]

Excellent….👍👍 Anyway, ur every work is just awesome .. Plus, I’m fond of ur electrifying lecturing style Best explanation..!!!

[@bentete6585]

there is a general method for generating Chinese magic squares of dimensions 3x3, 5x5, 7x7, 9x9 , ... and it"s good universally for integral sequence; evilkillerwhale has it in comment below

[@danfordaniel7896]

It says 369! The ! means factorial the amount of ways to position the numbers.

[@HemantPandey123]

1. Once we make 3 by 3 squares we can position them in any of the 9 squares. This will not disturb the whole combination. Hence this is not a unique solution and we can make 9! magic squares from these numbers only!! Swapping any two 3 by 3 square grid does not change the magic square. 2. Same method can be used for 6 by 6 or any 3n by 3n magic square.

[@HyperspaceGamer0]

I feel like this was some inspiration for sudoku

[@RiyadhAlDuwaisan]

stunning !

[@UFO314159]

9 x 9 magic square video is 9:09 long. Nice.

[@titansilva24]

Hi thank for you for this awesome video it is very clear. What is this magic square useful for?

[@kenyh575]

That is amazing. Thank you for sharing this the video clip. I did subscribe and thumb up LIKE

[@redgeoblaze3752]

I'm going to make a C++ program to make one for 81x81, I'll post the contents of the text document if it ever works

[@richardtowers6948]

I think you misspoke when you said every diagonal adds up to 369. There are 30 diagonals with more than 1 number in, but the only diagonals that add up to 369 are the 2 major diagonals.

[@AlecksSubtil]

Richard Towers Só há duas diagonais lá. A definição de diagonal é um segmento de reta entre dois vértices, não consecutiovos. Todas as outras linhas são oblíquas.

[@richardtowers6948]

Alecks Subtil Damn, you're right. Thanks Alecks. I was using the general definition:"Having a slanted or oblique direction". Really sloppy of me not to check whether "diagonal" had a specific mathematical meaning before I published my ignorance :-( I shall now slap myself diagonally 100 times.

[@AlecksSubtil]

I don't know why, but I swear i read your comment in portuguese. Maybe I was in the "automatic mode", haha. Nice you understood it!

[@richardtowers6948]

Alecks Subtil Well, Google did an excellent job of translation for a change. Your comment translated perfectly into English, which surprised me considering it was a technical special use of words.

[@phungcanhngo]

Amazing!

[@humblehombre9904]

Am I correct in assuming that how you write the numbers, as long as in order, makes no difference? Also turning, expanding, and compressing the numbers is just to keep from getting confused?

[@sumyiuli7803]

If you use the Lo Shu method twice, you have numbers in ascending order starting from the bottom.

[@popogast]

Is there a technique for a 7x7 or 5x5 magic square like this one? Or other prime numbers greater than 3?

[@gncgenz5829]

Don't forget every point in the individual magic squares make magic squares to

[@venkatachalamshanmugam7385]

Thanks Bass Good morning super

[@phrontisteries]

Dude, you're awesome! Thanks for all these posts! Any place I could go to see the math behind how/why it works?

[@MindYourDecisions]

Thanks. The 3x3 method was probably derived by brute force--I don't see any elegant reason for it. Then there are a few mathematical reasons for building the 9x9 square. 1. The 3x3 method works for any arithmetic sequence--any sequence of 9 numbers where you keep adding a constant to each term. So that's how we make the 3x3 small squares. 2. The 9x9 is built up recursively from the 3x3 squares. This makes sense since each 3x3 square is a magic square with a constant sum. So we can then position those squares according to the original 3x3 magic square and the sums will work out.

[@gamerlair1023]

+MindYourDecisions my logic reasoning for 3x3 square, 1st u add up all the numbers =45 because the 1st 3 horizontal rows must add up to the total , then divide by 3 = 15 (like taking average) which means each row/column adds up to 15. Now u decide if the corners should be odd or even. If the corners are all odd, the 1st row would be odd + even + odd = even, so it cant be the case, therefore the corners are even. Fill up even corners with 2 opposite of 8, then u can figure out what goes in the last 4 squares

[@clarkywilliamson8380]

This can be done in a different way as easy as counting if you know the direction format on any odd number square. 3x3. 5x5. 9x9. 11x11 an so on 😎. I actually learned how to do that back in the 60s !!!!!

[@namala3009]

1:27 smooth transition dude!

[@luvz2spluug3]

cool, now make a 81x81 magic square

[@fedorsykora272]

+luvz2spluug3 is it possible cause that was my question too

[@fedorsykora272]

+ads13000 nothing happend lol

[@fedorsykora272]

nice one

[@derciferreira7211]

+luvs2spluug3 it is possible to constructo any nxn square!

[@fedorsykora272]

+luvs2spluug3 how... I know post a video I m gonna give you like

[@josephcarbone5379]

Thank-you

[@frankieolmsted8448]

The corresponding parts of the smaller 3x3 triangles seem to make magic squares of their own. So, for example, if one arranges the top left element from each of the nine 3x3 square into a smaller 3x3 square, keeping the elements in their respective positions such that, for instance, the element which came from the bottom right square is in the bottom right of the new square, the rows' and columns' values add up to the same number. I noticed this for a few rows and conjectured it for the rest; someone smarter than I can endeavor to prove it true for all of them, if someone has a mind to.

[@royboggs4221]

The centers of each of the 3x3 grids is also a magic square.

[@Fogmeister]

If you take the numbers in the same position from each 3x3 grid it will make a magic square.

[@jakeames6840]

Fantastic Video!!! I want to make an 18 magic square. This will be 324. Will this method work for 18? Do I put 18 in each column and do the same technique as your video? Thanks.

[@Keshari2895]

Vow, thanks sir, you are very good teacher, but you have to explain us ABT their name, thought level, metal, emotion , how can they decided the name

[@JordanMetroidManiac]

The sum of the digits of 15 (from the 3x3 magic square) is 6. The sum of the digits of 369 (from the 9x9 magic square) is 18. Am I correct in assuming that the sum of the digits of the next integer (from the 27x27 magic square) will be 54?

[@MindYourDecisions]

+Jordan Fischer Interesting question. The 27x27 square will have the numbers 1 to 729. The sum of the numbers 1 to N is found by the formula N(N+1)/2. So the 27x27 magic square has the sum of all its numbers as 729(730)/2. Since each row and each column has to sum to the same value, we know each of the 27 rows has to be 1/27 of that number, which is 27(730)/2 = 9855. If I did the math correctly, the sum of these digits is 27. Using this method, the 81x81 has a row sum of 265761 which also sums to 27 and then the 243x243 has a row sum of 7174575 which sums to 36. Perhaps there are some patterns in this people might find out.

[@MauveTendingToBeige]

+MindYourDecisions to continue: 2187x2187 has a row sum 5230177695, which is the magic number, sums up to 45 6561x6561 has a magic number of 141214771521 which sums up to 36 19683x19683 has a magic number of 3812798752335 which sums up to 63 59049x59049 has a magic number of 102945566076849 which sums up to 72 So it seems that all magic numbers in the magic squares in the form of 3^n x 3^n are divisible by 3.

[@corinnelangan6634]

+MauveTendingToBeige they are all multiples of 9

[@ProProboscis]

Connor Langan Nope, not all, the first adds up to 6 not 9. Also: I thought there was a segment of hair on my screen, your profile picture tricked me.

[@toddbiesel4288]

MindYourDecisions The 729×729 magic square has a row total of 193710609, with a digit total of 36.

[@jontiong]

Can u tell me how many combinations of are there to solve these 9*9 magic square?

[@mspeir]

What's the ancient Chinese technique to make a Parker square?

[@manhdungo5562]

I think we can build another by : 1, build 8 other magic square by adding 9,18,...,72 to each number of the square 2, put each magic square on the position : first square on position 1 , "+9 square" on position 2,...

[@rajanilapatel]

EXCELLENT

[@mdsuruzzaman2014]

Will you please explain 10×10 magic square ? I can understand 9×9 magic square from your lectures . Thanks a lot.

[@damageinc5441]

There is no 10x10 magic square it goes 3x3 5x5 7x7 9x9 so next would have to be 11x11

[@kamleshpatel6652]

All 3*3-9 column calculation 369 perfect 1 to 81, but wrong pattern 🙏🏻 I have a calculation 1 to 100000000000000......................................... it's our Indian VEDIC maths 🎉 unstoppable 🙏🏻

[@NominalVentures]

Presh, thanks so much for the video. I just re-watched it yesterday. (originally saw it years ago) Can anyone confirm that the top-left cell value of an 6561 by 6561 grid, 8th-order Lo Shu Magic Square is 16142521? And that the characteristic row/col/diagonal sum is 141214771521? Thanks!

[@ismacreations..nps...8254]

Thanks

[@richardli5151]

is this the key to success in Sudoku

[@ravenhalcon5347]

This is a cool method but there is an easier one and it applies to all odd-numbered magic squares

[@fedorsykora272]

is there 81x81 magic square too???

[@physicswithtony3102]

Can someone tell, where this magic matrix could be used please?

[@GreatYue]

Is the Jspanese Sudoku copied from the Lo Shu idea?

[@LivingChords]

GreatYue Sudoku was invented by an American so probably not.

[@badchessplyr]

@@LivingChords lol . soduku is japanese word . american copied it's idea from japan and appropiated it and never gave credit to japan

[@LivingChords]

@@badchessplyr wikipedia disagrees

[@badchessplyr]

@@LivingChords you know wikipedia can be edited and not a legitimate source of info

[@LivingChords]

@@badchessplyr it's pretty reliable, especially when the article has substancial citations

[@CZghost]

And what about 12x12 magic square? Is there a simple way to make that one?

[@talonkarrde9904]

If you know what nested, or compound, magic squares are, then you can use this Lo Shu technique to create any nested square. For the 12x12, you could take a 4x4 magic square and use it with the 3x3 solution. Just remember that your template square will be 9x16, even though the result is 12x12.

[@thogarofold]

cound you not use this method to construct any magic square of the form (3^n)*(3^n) for n greater than or equal to one

[@bionichornet7784]

can i do same for 81 * 81 square?

[@liviuredd8074]

there is a 27x27 magic square?

[@kaushalkawatra8700]

Can you make a magic square of 10 by 10 -OR- 10+10 ????

[@drtalal3575]

I have base to fill any square even more than 1million

[@JuneAmang1]

You make it more difficult and confusing

[@michaelempeigne3519]

Using this technique, how do we make a 4x4 magic square ?

[@MindYourDecisions]

Michael Empeigne This is how to make a 4x4 magic square from a date - kzbin.info/www/bejne/rpbOp4GYpriebZo This website generates 4x4 magic squares from birthdays: mindyourdecisions.com/MagicSquare.html

[@thogarofold]

odds of doing this at random is 8^9/81! or about 2x10^-113

[@BigyanChap]

is there a unique solution each time?

[@Li-yt7zh]

maybe unique if you count infinite reflections as the same

[@vidzanallthat]

"Did you figure it out ...?"

[@UFO314159]

6:58 Take that, Sudoku!

[@shahnaz18]

😂 I get that...

[@motorhead6763]

Maybe find some practical use for this like codex etc...Shalom

[@martinshoosterman]

Could we use this to make an 81x81 magic square?

[@MindYourDecisions]

martinshoosterman That is a good question I haven't checked since it would take a lot of time. There is a method you can use for magic squares of any odd number (81x81 or any oddxodd). You start in the middle of the top row writing a 1, and then you go "up and to the right" for the next number. If you go over the top, start at the bottom. Or if you go to the right, then wrap around left. (Think about it like the Atari game Asteroids--mathematically it's the shape of a torus or a donut). This method works for any magic square of odd order: www.math.wichita.edu/~richardson/mathematics/magic%20squares/odd-ordermagicsquares.html

[@henk6172]

In theory it would work.in other words yes, math = theory

[@KasabianFan44]

martinshoosterman Yup, it would work perfectly :)

[@AlgyCuber]

martinshoosterman but we have to do in level: 3x3 --> 9x9 --> 27x27 --> 81x81 --> 243x243 --> 729x729 etc.

[@leightonjulye]

this is their concept of the solar magic square; all Egyptism

[@pepegasadge2977]

2:08 Yeah or you could just go back if didn't understand it!

[@Kine1.1.1.1]

not bad

[@koolasaurus4761]

odds are 81!

[@striminator2697]

What's so special of 369

[@shabbirvijapure1511]

Subtitles distrubs

[@che069]

This one is Not Chinese made this pattern. This grid is copy version of our ganeshlakshmi yantra vidhya astrological pattern

[@izandee]

thats my name

[@shummiqureshi2124]

My name is MOHAMMAD ARIF QURESHI from Karachi north nazimabad PAKISTAN I like it very much

[@priyaldevmurari4209]

It's not Chinese method it's indian method of ramanujam

[@melbalao2791]

imma create a 18 x 18 lo shu square 😂

[@melbalao2791]

i mean 81 x 81

[@sumyiuli7803]

Yeah, submit when you're done

[@pantherplatform]

Had to be a turtle because God given intelligence would've got them killed

[@mnorway7268]

Wouldn't it be easier to write the digits sideways? 123 456 789 ... and then rotate 45 degree clockwise? __1 _4 2 7 5 3 _8 6 __9

[@Ravenishish]

+M Norway It honestly depends if you prefer columns or rows if you're working on the bigger squares (see how he splits them up when doing the 9x9 square, if you did that with the 81 numbers for the layout you'd take the first column for the first sub square etc). It falls under the category of both work, just depends on how you like to lay out your work.

[@ashlor5066]

戴九履一 左三右七 二四为肩 六八为足 五居中央

[@yassinazab6187]

Pacific people Dai nine one Left three right seven Two four for the shoulder Six to eight for the foot Five Central

[@ashlor5066]

戴九履一 it should mean "9 is the hat, and 1 is for feet"

[@jennytan7656]

81(!!!!!!!!!!!!!!!!!!!!!!!!!!!!)

[@216V0]

no. now make a magic cube

[@Slasherx28]

watch in 1.5x. talks too slow.

[@sanjeevsingh-kf2vm]

Sorry sir for your information it's not chienese Algorithm It's Indian Algorithm By Dr. Ramanujan you can search it over internet or Ancient Books