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Continuing with my "I've been making puzzles for my now non-existent classes" threads, I've also made a magic square generator :D. 

Magic square are squares so that all the rows, columns (and usually diagonals) add up to the same thing. You can also do a magic square without the diagonals adding up to the same thing, or with just one diagonal... it's not hard to program. 

These are really fun, and if you make a harder one, you actually need to use some algebra to solve one. For easier ones, you can simply figure out the total sum first, and then work backwards: 

Here's one you can simply fill in by figuring out the sum. Here, the rows, columns and diagonals all have equal sums: 

Magic square.pdf

Edited by square_25
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Posted (edited)

Here's the solution to the one above: 

Magic square solutions.pdf

And here's a trickier one that you really are best off doing using a bit of algebra: 

Randomized magic square.pdf

I can also specify given "puzzle numbers," if you want to make a secret message, and I can do bigger magic squares (although I think past 4 by 4 they become a rather masochistic indulgence.) I also have fraction functionality and can specify specific types of numbers for at least some of the entries. 

If you want some magic squares, let me know... I gotta do SOMETHING with all this lovely code I have, lol. 

Edited by square_25
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8 hours ago, CuriousMomof3 said:

Actually I think my kid would like these better than the crosswords.  If you wanted to make a few, as tricky as you can, that would be much appreciated.  We can use lots of distraction.

I'll make you some of each :-). I'll do it later today. 

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Posted (edited)

Oh, I can also makes ones where the PRODUCT of each row, column and diagonal is the same. (If you know logs, you can see that this is mathematically the same problem, but I'm sure it doesn't feel this way to a kid.) Here's one: Randomized magic square.pdf

Edited by square_25
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22 minutes ago, CuriousMomof3 said:

I don't know logs, but that was fun to solve.  I'm going to show it to my kid.  I'm curious how he'll solve it.  I don't doubt that it will be faster than the way I did it.  

Would you like one without answers filled in??

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30 minutes ago, CuriousMomof3 said:

I don't know logs, but that was fun to solve.  I'm going to show it to my kid.  I'm curious how he'll solve it.  I don't doubt that it will be faster than the way I did it.  

Logs aren’t the right way to do it, by the way! It just makes it clear that it’s mathematically equivalent to a standard square (logs will make products into sums, but the numbers will become irrational...)

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Posted (edited)
2 minutes ago, CuriousMomof3 said:

I didn't actually try your harder addition square, so I have to think about that.  

Even with the easier ones, it’s true :-).

Here’s one way to see it: take an addition square, and take powers of 2 of each number. You’ll get a multiplication square :-). 

Edited by square_25
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On 6/3/2020 at 6:34 PM, CuriousMomof3 said:

As soon as he wakes up we’ll tackle that.

You wanted more, right? Do you want product or sum ones? How big a crossword and how big should the numbers be? Fractions or integers? 🙂

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Just now, CuriousMomof3 said:

Yeah, all that!  DS10 isn't picky.  

I think DS12 might like integers or fractions if the sum or product was obvious (e.g. if there was one complete row or column).  

Luckily, "Is there a complete row or column" is one of the settings, lol. It definitely distinguishes a tricky puzzle from a less tricky one. 

I'll make some tonight or tomorrow morning :-). 

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Just now, CuriousMomof3 said:

Yeah, I saw that you could make them with or without complete rows or columns.  DS10 definitely wants without.  Of course you could also send the without, and DS10 could just tell me the number to write in to turn them into "with" for his brother.  

Oh, it's all easy enough :-). Just one press of a button ;-). I just need to make some time to do it. 

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2 hours ago, OKBud said:

Oh yeah! Thanks 🙂

 

What kinds of numbers would you like? Do you want a product or a sum one? 🙂

Also, did you try the crosswords? 🙂

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42 minutes ago, square_25 said:

What kinds of numbers would you like? Do you want a product or a sum one? 🙂

Also, did you try the crosswords? 🙂

Anything goes for this one! 

Not yet, I have them printed though.

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Square! 

We **love** these!! 

If you make any more easier ones, where three squares in a row are filled in (with any size number) please post them for download. I'd _very_ happily pay you! We all loved doing some of these and the crosswords today.

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36 minutes ago, OKBud said:

Square! 

We **love** these!! 

If you make any more easier ones, where three squares in a row are filled in (with any size number) please post them for download. I'd _very_ happily pay you! We all loved doing some of these and the crosswords today.

Thank you! I don't need payment, although I may ask you all to test out my app if I ever do get around to making one :D. 

Do you want any variety? I can make bigger ones, or product ones, or something. Or with fractions or without. Or more crosswords. Any requests?? They are very easy to make, I just need to tell my randomizer what to do and it does it :-). And I'm so glad that someone's getting use out of them, even if I'm not!! 

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9 minutes ago, CuriousMomof3 said:

Oooooh oooooh I want to try out your app!  Pick me, pick me! 

Hahahah, don't worry, you will totally get to try my currently utterly nonexistent app... whenever it comes into being! 

Need any more puzzles for your kiddos for now? 🙂

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8 hours ago, CuriousMomof3 said:

My mathemagician has been pretty sleepy for the past few days, but I'll take them for the future.  

 

What kinds of numbers? Products or sums?

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12 hours ago, square_25 said:

Do you want any variety? I can make bigger ones, or product ones, or something. Or with fractions or without.

 

Yeah, that all sounds good 🙂  The only thing for DS is he needs that initial row to get started.

 

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21 minutes ago, OKBud said:

 

Yeah, that all sounds good 🙂  The only thing for DS is he needs that initial row to get started.

 

OK, I'll make some tonight :-). I can also teach you a trick for what you do if you don't have a full row! 

Do you want any more crosswords as well? 

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43 minutes ago, OKBud said:

 

Yeah, that all sounds good 🙂  The only thing for DS is he needs that initial row to get started.

 

By the way, do you own Beast Academy, @OKBud? I don't use them as a main curriculum, but they do have quite a few puzzles. And if I remember correctly, one of my local mathy friends who teaches at our local homeschooling center center they recently released books with nothing but puzzles. 

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14 minutes ago, square_25 said:

By the way, do you own Beast Academy, @OKBud? I don't use them as a main curriculum, but they do have quite a few puzzles. And if I remember correctly, one of my local mathy friends who teaches at our local homeschooling center center they recently released books with nothing but puzzles. 

No I had them all and sold them. Something about them... my kids, generally compliant, were completely unable to engage with BA. I'm sure because it looked like "Mom's trying to make school fun" to them. Whereas just sitting down and playing some game or doing some one-off puzzle is just us hanging out. 

I will honestly take any of the crosswords and magic squares you care to post, and definitely tell me how to do the ones without a full row (though I still want those 🙂 ) ...I figured one out yesterday just by plugging numbers in and using them to gage how close I was. But it's all Japanese to DS without the first row.

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Posted (edited)
6 minutes ago, OKBud said:

No I had them all and sold them. Something about them... my kids, generally compliant, were completely unable to engage with BA. I'm sure because it looked like "Mom's trying to make school fun" to them. Whereas just sitting down and playing some game or doing some one-off puzzle is just us hanging out. 

I will honestly take any of the crosswords and magic squares you care to post, and definitely tell me how to do the ones without a full row (though I still want those 🙂 ) ...I figured one out yesterday just by plugging numbers in and using them to gage how close I was. But it's all Japanese to DS without the first row.

I'll keep posting, and I'll also soon post the hexagon honeycomb grids, which are a fun skip counting exercise. I'm not done with those, though -- my level of motivation has kind of cratered, now that I've realized I probably won't be able to teach classes in the fall... but hopefully they'll be done soon. 

Actually, DD7 was also MUCH more interested in the puzzles I made for class than the BA books. She loves the comic books, but she literally never picks up the workbooks for fun. And I'm not going to insist, because insisting on fun math seems... not fun :-P. And it's not like she needs the practice. 

Not trying to sell you on BA, I swear -- just mentioning that they do have some puzzles! They also have some printables on the website that may feel more like one-offs. (And I know they have BA online, although since we're pretty minimal on screens, I can't say how those are.) 

Edited by square_25
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1 hour ago, CuriousMomof3 said:

My almost 10 year old likes the online version of BA.  I seem to have convinced him that it's a fun video game he can play as a reward for finishing his math curriculum.  This might be evidence that BA is not just for gifted children.  

I honestly don't think it is, if you run it at a level that's not very frustrating for the kids. I actually found that lots of kids enjoyed puzzles in my class, as long as they could get a handle on them. 

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Posted (edited)

@OKBud, let me explain how to do some of the ones with a missing row. Here's an example. I'll explain it to you with variables, but you'll obviously want to explain without variables to your student :-): 

Solving_magic_square.thumb.jpg.74f2345f9b3651e259ae477fb0ae6867.jpg

Here, the key observation is to note that the sum of the column involving y and the row involving y are the same. Since those both sums both involve a y, that means the sums of the other TWO numbers in that row and that column are the same. That is, 

98 + 79  = 105 + x, 

which allows you to find that x = 72.

If you are a bit suspicious, you can write down the sum for the row and the sum fo the column yourself and equate them: 

98 + 79  + y  = 105 + x + y

As you can see, the y's cancel out, and you can get again figure out x (even if you don't know any algebra.) 

Edited by square_25
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On 6/23/2020 at 3:20 PM, square_25 said:

Anyone need any more of these?? 

These are great! I’ve copied all of what you’ve created so far for a fun mini-unit for DS.

If you have the time / interest, I’d love to see something exclusively using “special numbers” - square numbers (a magic square squared?? 😅), Fibonacci numbers, Primes (obviously not via multiplication, but perhaps sums?), etc. 

My DS has just completed the BA 3 series, but even if he can’t solve these himself he’d appreciate finding the pattern as we solve together. 

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46 minutes ago, Shoes+Ships+SealingWax said:

These are great! I’ve copied all of what you’ve created so far for a fun mini-unit for DS.

If you have the time / interest, I’d love to see something exclusively using “special numbers” - square numbers (a magic square squared?? 😅), Fibonacci numbers, Primes (obviously not via multiplication, but perhaps sums?), etc. 

My DS has just completed the BA 3 series, but even if he can’t solve these himself he’d appreciate finding the pattern as we solve together. 

Do you want some product and some sum ones?

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1 hour ago, lulalu said:

Yes! If you are offering! 

Absolutely. They are very easy to make. What would you like? You can specify types of numbers, size, product or sum... 

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2 hours ago, Shoes+Ships+SealingWax said:

Both or either are great! Whichever is easier / more fun for you to put together.

They are both super easy. That's the joy of a randomizer ;-). So I'll make some of each... how big do you want 'em? Do you also want some crosswords or no? 

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2 hours ago, square_25 said:

Absolutely. They are very easy to make. What would you like? You can specify types of numbers, size, product or sum... 

Sums within 100 would be great

any size works 

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6 hours ago, Shoes+Ships+SealingWax said:

Both or either are great! Whichever is easier / more fun for you to put together.

Would you like a filled row/column/diagonal for an easy start or to have it trickier, without an obvious way to compute the sum? 

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10 hours ago, square_25 said:

They are both super easy. That's the joy of a randomizer ;-). So I'll make some of each... how big do you want 'em? Do you also want some crosswords or no? 

Not too crazy big. 3x3 or 4x4 is plenty - beyond that might get frustrating!

What are the crosswords? Like the BA puzzles where numbers are shared & you have to complete the equivalencies? 

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7 hours ago, square_25 said:

Would you like a filled row/column/diagonal (to have a good way to start) or no? 

Maybe just one or two squares filled in. 

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8 hours ago, Shoes+Ships+SealingWax said:

Not too crazy big. 3x3 or 4x4 is plenty - beyond that might get frustrating!

What are the crosswords? Like the BA puzzles where numbers are shared & you have to complete the equivalencies? 

Yeah :-). There’s another thread around with lots of examples.

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