Unlocking the secrets of Magic Square puzzles
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- Опубліковано 13 чер 2024
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Magic Square puzzles are some of my favourite recreational math puzzles. Fill up a 3x3 square with the numbers 1 through 9 each used once so every row, column, and main diagonals add up to the same number. More generally, it can be a nxn square with numbers 1 through n^2, and there are actually tonnes of variants of these. In this video we will prove that there is precisely 1 possible 3x3 magic square (up to reflections and rotations). We'll do this by computing the Magic Number, aka the fixed sum each row must add up to, then figuring out the center must always sum to 5, and finally show how we get a single possible square. What's a bit crazy is that 4x4 has 880 possibilities, 5x5 has over 275 million possibilities, and for 6x6 it is so large we've never computed the exact number!
0:00 What is a Magic Puzzle?
0:45 Try these Magic Puzzles!
1:29 Ad hoc solving
2:27 Our 3x3 theorem
3:04 Gauss' counting trick
4:14 Sum formula
5:55 Central Square
7:09 Proving the theorem
9:25 Bigger magic squares
10:19 Brilliant.org/TreforBazett
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Watch my videos about real magic squares.
Constraint Programming is one of those topics I wish was higher in my learning priority queue.
Algorithm for solving any magic square with an odd number of squares on each side.
1. Place the numbers from 1 to n^2 in order.
2. Place 1 in the top middle square.
3. If the square up one and one to the right is open, next number goes there.
4. If the square up one and one to the right is outside of the magic square, then wrap around to the opposite side.
5. If no square is available, next number is placed one square down.
Well, this will make sudoku infinitely easier.
Ha it does help a bit in the ideas but not really for solving it tbh
9:28 thanks man now i can write all 8 magic square by just memorizing one
Got the first one quite easily, exactly the way he did after I hit play again. Need to take longer with the second one. I am 81 and have lost the ability to keep track of multiple steps mentally. I start out well, but will suddenly forget where I was going with it. lol It is still fun to try.
Really interesting!!! Thank you so much!
Sir, I love the way you teach math in very simple and exciting way .....I have started to love and enjoy math .......which I feared a lot.......Thank you so much......lots of love.....😀😀
And so... We know how many possible combinations have 6x6 (and even bigger!) rubik's cubes, but we don't know how many combinations does it have a 6x6 magic square? We (humanity) know many things, but we still don't know and understand how many things in the universe!
My understanding is the limitations here are mostly computational with the limits of modern computers
...A failed attempt at the magic square gives you a PARKER SQUARE.
😂
Jokes aside, I can't wait to learn through your content.
excited to study mathematics/ physics/ mathematics and computing subjects at university.
[I'll be done with my entrance exams by 3rd week of June :) ]
hope i get my desired university
Fingers crossed 🤞
:D That's awesome though, you are going to be amazing at uni!
the thing is, the term Parker Square has actually already been used in a mathematical research paper, making it a canonical term
@@wyboo2019 cool ...
I wasn't aware of this
So, there is only one permutation to the 3x3, but as the size increases, is there a recognizable pattern in the growth of the number of allowable permutations? I mean, only up to 5x5 has been solved, but it seems like there should be a mathematical pattern, or is it because only a very tiny number have had their permutation possibilities calculated that there isn't a direct pattern distinctly seen yet?
Exactly!
Love the t-shirt ,it reminds of a homer simpson quote "remember your hippopotamus oath"
That shirt is awesome!!!
Niceee professor 😃😄
Thank you!
I already knew about Magic squares; CTC did a buzzle of more than 4 in a single puzzle.
Im proud that I proved you can only have 8 solutions for the 3×3, on my own.
سبقك الاستاذ انور 😅
Thank you, 3x 3 and 4x 4 are fairly easy. How about 5 x 5 and 6 x 6 . There is also other numbers than 1 to 9. Any consecutive 9 numbers (-5, - 4, -3 ...1, 2, 3, 4). The center number is the sum of the numbers divided by the number of cells
For the 4 * 4 magic square, it took me a while to figure out what the numbers were because I used the ad hoc method.
Ya for sure, a lot of the 4x4 puzzles you gotta play around and try different ideas to see the one that works.
@@DrTrefor yep some of the numbers didn't quite add up to 34 and some of the numbers when inserted would require using a number already in the magic square. So I had to tinker with the numbers until it all the rows, columns and diagonals added to 34.
That seemed very complicated for how to do the puzzle, not sure I gained the solution in a way I was expecting.
Professor How about if the question is everything should have the same total but using multiplication?
Actually when I googled, I stumbled upon this:
JULY 2023:
"Prof. Hidetoshi Mino has counted the magic squares of order 6 to be 17,753,889,189,701,384,304 different 6x6 magic squares."
That's pretty new.. but yeah, now we know.
Also, the sum of all numbers in a 6x6 magic square is sigma 36 which is equal to 666, which is kinda cool lol.
does it have to do with -1/12= 1/2
First comment proffesor. 💓
It is also the ancient tradition of India. Which was also developed by Srinivasa Ramanujan
Nice one!
the cent .5/ 5 = 1/2 = half why is the center number five equal .5 half or 5 or use 4 times as is used with other edge digits.. to =15
odd numbers always have to be in the center, and even numbers always end in the corners...
Here's what I got for 0:45~1:03 before watching the rest of the video.
3x3
8,3,4
1,5,9
6,7,2
4x4
7,13,12, 2
10, 4, 5,15
1,11,14, 8
16, 6, 3, 9
The video confirms that my 3x3 solution is correct, but what about my 4x4 solution?
Your 4x4 is good! And you can confirm it by double checking the rows/columns/diagonal all do add up right.
@@DrTrefor I tried doing that, but I would sometimes lose track of which ones I checked and which ones I didn't. Additionally, I wasn't entirely sure that I had typed them into the calculator properly.
Do you watch Cracking the Cryptic?
aaaaaaaa I need to know if my solution to the other grid is right or I'm just blind and can't see my mistakes as always
The opening is not explained. Why does a 3x3 magic square have to contain all the digits between 1 and 9 used once and only once? That seems to be what the video is saying but I thought it could contain any numbers.
I’m asserting this as the definition of the puzzle we are analyzing
why does it come up 15, if decimals 1.5 = 1+ 1/2
101 Dalmatians. lol.
()K, Eye Cee, solves mANy A di-lemma. Lemniscate, a plane to C
I thought magic squares could have any numbers in them, not just 1...n.
There are lots of variants, so the specific theorem I did for this video needs everything from 1 to n, but there are many closely related one
Damn bro I'm early
Ha nice!
Before Christ*
Christ doesn’t matter other than as a historical figure that might be real that we kinda sorta use as an anchor for dates. He’s maybe just a dude that hoodwinked a bunch of fools to write stories.
@yumnuska Jesus Christ is the son of God/ God the son, the man who died a brutal death on the cross to give all of us something we don't deserve, which is a spot in heaven, the chance to become a child of God if you accept Him as your Lord and Saviour
So please give Him some respect, and please consider maybe giving your life to Him😊