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The Magic Cafe Forum Index » » Magical equations » » Bill Fritz' "Magic Squares for the Mathematically Challenged" (0 Likes) Printer Friendly Version

Scott Cram
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Bill Fritz (Mr. Mindbender) has just generous shared some amazing work on the magic square with the community...and he's shared it for free!

He's dubbed it "Magic Squares for the Mathematically Challenged", which comes as a set of lecture notes (downloadable via the link in the post) and 8 screencasts. The notes and screencasts are available on my blog.

He's taken the standard foundation magic square approach ((X - 34)/4), and made the math muuuuch easier to do! Don't believe me? Watch how quickly he works out the answers in the first screencast (in the blog entry)! I don't know of anyone who could do the math as fast as his system gives you the needed numbers.

He also gives more details on his Post-It Note magic square presentation in the final section and screencast.

Bill, thanks again for generously sharing this work!
TomasB
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This isn't math-less but I made it so that the only two potentially hard calculations is to divide an _even_ number in half. Heck, even I can do that with 3-digit numbers in my head. Smile

Memorize the 1 through 12 order in the magic square. Also memorize the order of the last four squares you'll fill in.

Code:
<br> 8   11  B   1
<br> A   2   7   12
<br> 3   D   9   6
<br> 10  5   4   C
<br>


When someone names a number, subtract 30 from it.

Make sure it's even by evening it up by removing one if needed.

Take half.

Make sure it's even, by removing one if needed.

Take half.

This is the number you fill in cell 1 and simply continue filling in the first 12 cells seqentially.

Now is the only place you may have to make a bigger step.

If you never needed to even a number up, just step one.
If you evened up before the first division, step two.
If you evened up the second division, step three.
If you evened up both times, step four.

That's an order easily rembered by simply remembering that the second evening up is "worth" more. The rest of the rules above become obvious then.

Fill in the last three sequentially.

Example: They name 423. Subtract 30 to get 393.

393 is hard to divide so call it 392 instead. Divide to 196.
196 is easy to divide so divide to 98.

Fill in the first 12 cells:

Code:
<br>105 108  B   98
<br> A   99 104 109
<br>100  D  106 103
<br>107 102 101  C
<br>


Since we only adjusted the first division we have to step 2, so A will be 111 to make the finished square

Code:
<br>105 108 112  98
<br>111  99 104 109
<br>100 114 106 103
<br>107 102 101 113
<br>


If you limit them to two-digit numbers, dividing an even two-digit number by two is really easy.

/Tomas
OldNick
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Thomas: Wow! This is beautiful!

Thank you very much for sharing this!
Roland
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TomasB
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Here you can see my algorithm in action live, by the fantastic Peter Gröning: http://www.youtube.com/watch?v=yNZ9wkE8yJE

The rapid counting explanation is in Swedish so it might be a bit hard to understand, but he claims to have taken some mental snapshots and divided the problem into four quadrants. That of course makes it much easier to count in the mental snapshots. Smile

The idea to combine pain with the ability is by Luke Jermay.

/Tomas
landmark
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I believe that concept was Derren Brown's--I've seen a clip from one of his stage shows with the same slapping idea.
TomasB
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Guess who the consultant was for Derren's show? Smile

/Tomas
landmark
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Ahh. My bad.
The Magic Cafe Forum Index » » Magical equations » » Bill Fritz' "Magic Squares for the Mathematically Challenged" (0 Likes)
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