For anyone who are still interested, some fundamental concepts related to this to share. (report this as spam or something if I'm spoiling too much of the fun.) Using consecutive numbers is a constraint that actually makes things a lot simpler. 25 consecutive numbers only works for adding up to multiples of 5. Its basically similar to summing up numbers from 1 to 100 (1+2+...+99+100), where 50 pairs of numbers give same value of 101. In this case, groups of 5 numbers are involved instead. And it is easier to do the "reverse manner", working through the complement (set theory). Although this can be performed by anyone, without fully understanding the "theory" behind it, by just following the pattern. Still, hope more people can appreciate the arithmetic in this, simple yet fascinating.
Magic squares exist for all sizes, there are a few methods for constructing them. And in this video I used a more complicated method than just altering the last n.
So basically, you start in the middle. You move 2 squares up and 1 square right. If you move out of the square, you just end up on the opposite side. When you've done that 4 times, 2 up and 1 right will put you back in the middle, so instead you go down 1 square. (From this square, you would have to go 3 squares up an 1 right to get back to the middle.) This algorithm repeats until the grid is full, with the last number right above the middle square you started in. Using numbers 1-25 gives you a magic square with sums of 65. So by subtracting 4 from each number you got sums equal to 65 -4*5=45 (making the nice of trick putting in the minuses after filling each square possible). And when you wanted 68, you just skipped three numbers in the sequence, going directly from 20 to 24, instead of having 21 as the next number, meaning the sums become 65+3=68. Edit: added missing words.
Improbabilities almost right. but your theory is dead when you look at the number 1 and 2. they don't follow the rules you made (well 1 does, but 2 doesn't)
Ramhams1337 You go down from the bottom, looping around to the top, and keep going. 1 is at the bottom and 2 is at the top, right "beneath" the number 1 according to my rules. I don't see how that contradicts my theory.
Improbabilities how you said it made it soud like you meant going down 1 from the space occupied if it was occupied, and not from your original spot. that's why it was countradicting it. you need to explain better then butit fits with what you are saying then
what is the mathematics behind the 4x4 and the 5x5 square. To create such a square I imagine you take a standard magical 5x5 square and add or subtract a certain number from it to create a magical square for the specific number in question.
Hi Jim, It's arthritis, I cannot understand why it works, ie. how does this mechanism of building the magic square work. Can we actually build magic squares of nxn of any size? And do they all work on the principle of determining the values of n^2-n of the elements in the magic square?
Well, I made a similar magic square for a sum of 91, but that was a little too easy. Is there really a way to calculate this or was 68 a little less than random?
@singingbanana You should add an annotation"19" over the top left corner number for the from :41 to 3:14. This would prevent people from mistakenly thinking that it is a "14"
I guess what Error was talking about was an increase of modular 4, in each of the 20 non-calculated numbers, yeah, I solved 90 and 89 as well. But guess was still a little dissatisfied, is there an algorithm to work out the way the numbers should be placed and why does it work that way?
nice vid and a clever idea to use an easy trick. did you try other square sizes? at the first moment it looks like it works in any size, but im not sure if all combinations like the crosses still work. cant find a quick solution for that =(
And I begin to understand why those 5 numbers have to be in those specific locations. Because in those locations, each diagonal/ combination of 5 number will only have one number which is calculated. But i still cannot understand why the rest of the numbers move the way they do?
It's actually fairly easy when you see the system. It took me a while to figure out how to start out and how to adjust the last five numbers without the need to reuse previously used numbers. Thanks for this little brain tease.
I have noticed that you (somehow) find out what the lowest number in the grid should be (In the first case -3). Now you do knight's moves: Up 2, over 1. BUT if you land on a number you already wrote down (ex. in the first one 1 goes back to -3) you put the next number (2) underneath (2 goes under 1). Continue. I have noticed in the second one it jumps from 20 to 24. This is all I found out so far
Yes, you are the only one who's mentioned that. The second one isn't consecutive, and there is formula. There's a formula for the whole thing, but this once I'm going to be a magician and keep the secret (but that doesn't stop you finding out).
The second example seems to be exactly like the 4x4 in the other video, and involves the number 42 (or 44, depending on how you think about it...). I'm still thinking about the first example - that's quite different, or seems to be...
I was hoping you would post a new video soon. I regret it now. I'm either going to spend the rest of my day puzzled about this or just go cry in a corner. I havn't decided yet which to do.
You should add an annotation"19" over the top left corner number from :41 to 3:14. This would prevent people from mistakenly thinking that it is a "14"
That was awesome! Naturally everyone is going to try and find a flaw. I first saw your pi trick on scam school. I really enjoy math and Hope I can do some of these things one day
I wonder if we do this the same way. I know you've seen my excel program which does it, but I've only just taken to doing it by hand. If we do this the same way, you are very fast. It takes me about 5 minutes right now, and I certainly couldn't talk coherently during the operation.
Ok, after doing a little magic square research and then coming back and comparing the two squares you did...I think I could replicate this type of square, but I would have to start writing a number in the center and move in a pattern, whereas you (impressively), were not doing that. I really like the video - great food for thought.
I almost understand it. If u have the first number the magic square revealed! If a square has a (x) number and u go 2 squares down and 1 right the number in the square is x-5 (and the -5 is there, obviously, because the magic square is 5x5). My problem is how u find the first number. I hope that i will solve this problem soon
Basically, you start in the middle (I don't think you have to, but since James did, this case will be easier to compare with the video). You move 2 squares up and 1 square right. If you move out of the grid, you just end up on the opposite side. when you've done that 4 times, 2 up and 1 right will put you back in the middle, so instead you go down 1 square. this algorithm repeats until the grid is full, with the last number right above the middle square you started in. Using numbers 1-25 gives you a magic square with sums of 65. So by subtracting 4 from each number, James got sums equal to 65 -4*5=45 (making the nice of trick putting in the minuses after filling each square possible). And when he wanted 68, he just skipped three numbers in the sequence, going directly from 20 to 24, instead of having 21 as the next number, meaning the sums become 65+3=68.
Yes Jim, but you are still using the same principle. This is what i noticed, There are only 5 numbers that you are determining, the rest of the 20 numbers move in a modular fashion. Let a,b,c ...denote the column Let 1,2,3 ...denote the ranks
the numbers you are calculating are a1, b4, c2, d5, e3, the rest of the elements are actually modular of each other ( i.e. +4) in each number. Can you do a third 5x5 sequence for us to see how you determine the modulus interval?
There are definitely patterns in the method you used to construct those two squares, though you did hide them a little. I don't feel like analyzing it at all right now, but if or when I do, your secret is safe with me.
Do a magic square = 65 using numbers 1 - 25 you can only use each number once and only using addition / post a video of you doing it for the first time and see how long it takes you
Once you see the pattern, this is actually quite fast to generate. The only problem is that if it's done the intuitive way in front of an audience, everyone would instantly see the trick. :D So it's probably unavoidable to have to mix the order around a bit to make it less obvious and that will require some concentration.
There is a fairly simple algorithm to this 5x5 magic square. Notice where he starts out and you will find that the square 2,2 (row,column) is important.. Sorry singingbanana i could not resist..
For anyone who are still interested, some fundamental concepts related to this to share. (report this as spam or something if I'm spoiling too much of the fun.)
Using consecutive numbers is a constraint that actually makes things a lot simpler.
25 consecutive numbers only works for adding up to multiples of 5.
Its basically similar to summing up numbers from 1 to 100 (1+2+...+99+100), where 50 pairs of numbers give same value of 101. In this case, groups of 5 numbers are involved instead. And it is easier to do the "reverse manner", working through the complement (set theory).
Although this can be performed by anyone, without fully understanding the "theory" behind it, by just following the pattern. Still, hope more people can appreciate the arithmetic in this, simple yet fascinating.
I'm blown away by your mathematical prowess to make such a great magic square so quickly...
I don't have that particular book, but by the sounds of it I probably have a lot of that material in other books.
Magic squares exist for all sizes, there are a few methods for constructing them. And in this video I used a more complicated method than just altering the last n.
Hey there! Could you show us how you did it
have you made a tutorial on this 5x5 and if not will you do it?
So basically, you start in the middle. You move 2 squares up and 1 square right. If you move out of the square, you just end up on the opposite side. When you've done that 4 times, 2 up and 1 right will put you back in the middle, so instead you go down 1 square. (From this square, you would have to go 3 squares up an 1 right to get back to the middle.) This algorithm repeats until the grid is full, with the last number right above the middle square you started in.
Using numbers 1-25 gives you a magic square with sums of 65. So by subtracting 4 from each number you got sums equal to 65 -4*5=45 (making the nice of trick putting in the minuses after filling each square possible).
And when you wanted 68, you just skipped three numbers in the sequence, going directly from 20 to 24, instead of having 21 as the next number, meaning the sums become 65+3=68.
Edit: added missing words.
Improbabilities almost right. but your theory is dead when you look at the number 1 and 2. they don't follow the rules you made (well 1 does, but 2 doesn't)
Ramhams1337 You go down from the bottom, looping around to the top, and keep going. 1 is at the bottom and 2 is at the top, right "beneath" the number 1 according to my rules. I don't see how that contradicts my theory.
Improbabilities how you said it made it soud like you meant going down 1 from the space occupied if it was occupied, and not from your original spot. that's why it was countradicting it. you need to explain better then butit fits with what you are saying then
Ramhams1337 I see what you mean. Communication is hard! I added a sentence (in parenthesis) for clarity. Thanks for pointing it out.
Improbabilities is
what is the mathematics behind the 4x4 and the 5x5 square. To create such a square I imagine you take a standard magical 5x5 square and add or subtract a certain number from it to create a magical square for the specific number in question.
The number in the top left corner is 19 not 14.
Hi Jim,
It's arthritis, I cannot understand why it works, ie. how does this mechanism of building the magic square work.
Can we actually build magic squares of nxn of any size? And do they all work on the principle of determining the values of
n^2-n of the elements in the magic square?
Well, I made a similar magic square for a sum of 91, but that was a little too easy. Is there really a way to calculate this or was 68 a little less than random?
@singingbanana You should add an annotation"19" over the top left corner number for the from :41 to 3:14. This would prevent people from mistakenly thinking that it is a "14"
would you mind explaining how exactly this works?
Why do you move the pen out of shot after eat number is written?
are you going to reveal how this is done? pls
Is it possible to construct a 3 dimensional magic cube?
Do you gone expain how your are doing this
Please tell me how to do that before I melt!
you amaze me man!!!!
I guess what Error was talking about was an increase of modular 4, in each of the 20 non-calculated numbers, yeah, I solved 90 and 89 as well.
But guess was still a little dissatisfied, is there an algorithm to work out the way the numbers should be placed and why does it work that way?
can u teach me to do pub in tricks??
nice vid and a clever idea to use an easy trick.
did you try other square sizes? at the first moment it looks like it works in any size, but im not sure if all combinations like the crosses still work. cant find a quick solution for that =(
And I begin to understand why those 5 numbers have to be in those specific locations.
Because in those locations, each diagonal/ combination of 5 number will only have one number which is calculated.
But i still cannot understand why the rest of the numbers move the way they do?
Please explain how to do this.
By the way...I agree with doughside, that marker is annoying.
@xxstrxxnowxx where is your tutorial?
@rafathama Yes, it does.
You can find out more about background history on Magic Squares in art, science and culture on Glenn Westmore's blog.
It's actually fairly easy when you see the system. It took me a while to figure out how to start out and how to adjust the last five numbers without the need to reuse previously used numbers. Thanks for this little brain tease.
I have noticed that you (somehow) find out what the lowest number in the grid should be (In the first case -3). Now you do knight's moves: Up 2, over 1. BUT if you land on a number you already wrote down (ex. in the first one 1 goes back to -3) you put the next number (2) underneath (2 goes under 1). Continue. I have noticed in the second one it jumps from 20 to 24. This is all I found out so far
Thank you as always Eric. By the way, did you know you're tweeting all you're comments?
Yes, you are the only one who's mentioned that. The second one isn't consecutive, and there is formula. There's a formula for the whole thing, but this once I'm going to be a magician and keep the secret (but that doesn't stop you finding out).
The second example seems to be exactly like the 4x4 in the other video, and involves the number 42 (or 44, depending on how you think about it...). I'm still thinking about the first example - that's quite different, or seems to be...
Wow, now this is really impressive. Genius really....I'm blown away.
I’m here for homework
but how do you do it its not a tutorial if you dont explain >.<
can some one plz mak a tutorial?
Please post a tutorial!
I was hoping you would post a new video soon. I regret it now. I'm either going to spend the rest of my day puzzled about this or just go cry in a corner. I havn't decided yet which to do.
You should add an annotation"19" over the top left corner number from :41 to 3:14. This would prevent people from mistakenly thinking that it is a "14"
It's 14only
That was awesome! Naturally everyone is going to try and find a flaw. I first saw your pi trick on scam school. I really enjoy math and Hope I can do some of these things one day
I wonder if we do this the same way. I know you've seen my excel program which does it, but I've only just taken to doing it by hand. If we do this the same way, you are very fast. It takes me about 5 minutes right now, and I certainly couldn't talk coherently during the operation.
FINALLY AFTER 2 FULL YEARS I FIGURED OUT HOW HE MADE IT, ITS ACTUALLY QUITE EASY
How the hell does he do that?
how you do that too fast?????
Will you post a tutorial on this?
I already amazed my algebra teacher with the 4x4. Maybe I could make his jaw unjoint when I show him this ;D
did you use some kind of algorithm to do that.?
@TheLittleHousePA the top row doesn't add up to 45 either
68 was random, first two cards out the pack, just as I presented it.
please make a tutorial!
Ok, after doing a little magic square research and then coming back and comparing the two squares you did...I think I could replicate this type of square, but I would have to start writing a number in the center and move in a pattern, whereas you (impressively), were not doing that. I really like the video - great food for thought.
@joshi12311 top row, 19+2 = 21, 21+15=36, 36-2=34, 34+11=45, What the hell did you type in your calculator?
Thank you. Blame writing quickly in felt tip. My '4's look different to that.
It wasn't a tutorial. It was a response to a tutorial. That why I called it that.
there is something wrong with your first square.the first row isn't adding up to 45 or is it just me?
I'm confused. You wrote down 65 , but you added 45 at the magic square. Did I miss something?
@joshi12311 The second 2 is a negative 2. So it is 45. You punched in 19 +2 +15 +2 +11, but its 19 + 2 + 15 -2 + 11.
@Error081688 Neither did I!
@weflylow2183 Uhm my friend got on my youtube and deleted it to be a jerk a while ago. want me to re upload it?
What a coincidence, just this morning, going to school, i was thinking on creating a magic square and how it works. Cool.
Does James Grime own SINGINGBANANA?
I almost understand it. If u have the first number the magic square revealed! If a square has a (x) number and u go 2 squares down and 1 right the number in the square is x-5 (and the -5 is there, obviously, because the magic square is 5x5).
My problem is how u find the first number. I hope that i will solve this problem soon
Yup. I've just practiced :)
Can you please tell me how did you did this ?
Basically, you start in the middle (I don't think you have to, but since James did, this case will be easier to compare with the video). You move 2 squares up and 1 square right. If you move out of the grid, you just end up on the opposite side. when you've done that 4 times, 2 up and 1 right will put you back in the middle, so instead you go down 1 square. this algorithm repeats until the grid is full, with the last number right above the middle square you started in.
Using numbers 1-25 gives you a magic square with sums of 65. So by subtracting 4 from each number, James got sums equal to 65 -4*5=45 (making the nice of trick putting in the minuses after filling each square possible).
And when he wanted 68, he just skipped three numbers in the sequence, going directly from 20 to 24, instead of having 21 as the next number, meaning the sums become 65+3=68.
+Improbabilities Thanks
Yes Jim, but you are still using the same principle. This is what i noticed,
There are only 5 numbers that you are determining, the rest of the 20 numbers move in a modular fashion.
Let a,b,c ...denote the column
Let 1,2,3 ...denote the ranks
the numbers you are calculating are a1, b4, c2, d5, e3,
the rest of the elements are actually modular of each other ( i.e. +4) in each number.
Can you do a third 5x5 sequence for us to see how you determine the modulus interval?
Yup, those are the nice 'pattern' sums. There are a thousand more, just not in nice patterns.
I think he gets the nos. 1 to 20. then uses 5 other consecutive nos. to get the certain number.
That was great, hope you post more vids like this, give our brains a good workout you know, as we try and discover how you do it =D
Peace
@weflylow2183 Alright i gate go to work right now so ill upload it when ill get back. The method i use is the one he does on the second 5x5 one.
It is ont right if you check all this boxes they arent all add 45
There are definitely patterns in the method you used to construct those two squares, though you did hide them a little. I don't feel like analyzing it at all right now, but if or when I do, your secret is safe with me.
@vssnfrankiej It is 19+2+15-2+11=45, the second two is actually a -2.
Do a magic square = 65 using numbers 1 - 25 you can only use each number once and only using addition / post a video of you doing it for the first time and see how long it takes you
my mind EXPLODED
@xLittleVinnie sry, dont saw the "-" thought it was "+" ^^
make a tut
what does he mean, the cross form the two diagnols adds up to 45? i get 93..?
That's very cool. You're not going to even hint at the algorithm you use?
Er... 42?
Could you do a tutorial for this...say...at 5000 subs?
Panmagic squares are the best, you get the idea :)
Woah... I'm impressed!
Oh no, wait - I get it now :) Nice touch, subtracting to get the negative numbers. Neat video!
Once you see the pattern, this is actually quite fast to generate. The only problem is that if it's done the intuitive way in front of an audience, everyone would instantly see the trick. :D So it's probably unavoidable to have to mix the order around a bit to make it less obvious and that will require some concentration.
its cool that you got featured on scam school for the 4*4 magic square
in big plus u only take middle and last numbers in plus arms, u always take only 5 numbers and add em...cheers
i am pretty sure the top row doesn't come on 45....
19+2+15+2+11=49
correct me if i'm wrong:$
@rafathama the 14 you say of is a 19
That was an incredible slip of the tongue. Doh.
why are you taking your hand away all the time? like you are using another one which is premade
@imorio it's 19, not 14... -_-
WTF?! You are really smart. If I tried that I would probably put down two numbers and realize that I did it wrong and have to start all over.
That's 19 top left.
Nice panmagic square... ;~b
Funny enough, I can see a method close to De La Loubère's.
With some adaptations to get the sum you want. Nice trick.
I CANT CALCULATE THE WHITE DOTS !!!!!!
your so SMART!
I guess if you were to start placing the numbers from 1 to 20, you would start with the centre
@rafathama its a 19 not a 14
Maybe one day. It can happen.
@TheLittleHousePA Well, good job that doesn't say 14 then.
There is a fairly simple algorithm to this 5x5 magic square. Notice where he starts out and you will find that the square 2,2 (row,column) is important.. Sorry singingbanana i could not resist..
everyone thinks the top left hand corner says 14 its 19 people