How can I solve this problem?

Ion · 2010-05-23 21:31:47

Problem is:

x(A-1)+B=y

If x=9 and y=28 how much is A and B?

Thank you.

bobbym · 2010-05-23 21:38:11

Hi Ion;

You have

9(A-1)+B = 28

9A - 9 + B = 28

9A + B = 37

You have 2 variables and 1 equation that means you will an infinite number of solutions here.

B = 37 - 9A

or

A = (37 - B) / 9

Take the first equation. Now pick any A you want. For instance A = 2 then B = 37 - 18 = 19
or A = 1 then B = 37 - 9 = 28 or A = 0 then B = 37.

You see there are an infifnite number of solutions. You can graph the equation B = 37 - 9A and you will see it is a straight line.

Ion · 2010-05-23 21:54:16

Thank you bobbym.

I start to read about Lo Shu squares and I have found this way of building a 9x9 bimagic square from 2 Sudokus with the formula x(A-1)+B=y by Tarry-Cazalas method as you can see in the link below:

http://www.taliscope.com/LoShu_en.html

I was trying find out a way to determin the Sudokus if I know only the 9x9 square.

bobbym · 2010-05-23 21:59:37

Hi Ion;

He is not referring to scalar quanties but to A and B being matrices of sudoku squares.

Ion · 2010-05-23 22:15:32

Thank you bobbym, your answer helped a lot.

bobbym · 2010-05-23 22:17:48

Hi Ion;

When you see A and B like that (capitalized) they mean matrices. He is multiplying the A matrix by 9 and subtracting 1.

Ion · 2010-05-23 22:54:12

Hi bobbym;

I appriciate your answer and help.

If i know one of the matrix is easy to determine the second one by the solution you give me.

Don't know how to determine both matrices if I see only the 9-th order square.

bobbym · 2010-05-23 23:05:11

Hi;

I think he is saying you need to start with with 2 sudoku magic squares. Are you able to generate 1 of them?

Ion · 2010-05-23 23:52:28

Hi bobbym,

I don't know how to generate 1 of them. Can you tell me where i can find something to read about this please!?

As far as i understand the numbers work as a vortex around 5 on clasic 3x3 lo shu. I know how to generate a Sierpinski fractal 1-81 but this does'nt helped me so far to understand how sudokus are generated.

Thank you.

bobbym · 2010-05-23 23:56:21

I have a program to solve them or generate them. Off hand I don't have an algorithm for it. have you tried googling it

Ion · 2010-05-24 00:06:31

I like it very much so i'll keep looking.

bobbym · 2010-05-24 00:23:18

On this page I am looking at;

http://davidbau.com/archives/2006/09/04 … rator.html

There is a guy who describes his method to make them. It is near the bottom. It might help. They are a particular type of latin square.

Ion · 2010-05-24 00:37:37

Good stuff to read. Thank you again bobbym.

bobbym · 2010-05-24 00:41:43

Please come back and tell me how you solved it when you do. And welcome to the forum!

Ion · 2010-05-24 00:47:36

I will do that. Glad to be around.

Ion · 2010-05-25 01:42:12

Hi bobbym,

Yesterday I saw that the value of B matrix is the same as the sum of the corespondent value in the 9x9 bimagic square.

http://www.taliscope.com/LoShu_en.html

Take 28 as final value as my example, 2+8=10=>1+0=1=B.
All the square works the same.
From here by the formulas you gave me is easy to determine A matrix.

Check out this link:

http://www.multimagie.com/ (in the left side go to Bimagic Squares 9)..

..take the problem put by G. Pfeffermann in 1891(bi-trimagic square) and split the matrices as I said and you will find some interesting things going on with the the numbers graviting around number 5.

bobbym · 2010-05-25 02:11:05

Hi Ion;

I am having problems getting that page to load for me. If you have time can you show me what you mean?

Ion · 2010-05-25 02:25:59

No problem bobbym, just let me know when you get it please.

bobbym · 2010-05-25 02:38:59

Okay, I have it. I am looking at Pfeffermann's incomplete bi magic square. I see what you mean with the formula

9(A - 1) + B and 9(B - 1) + A.

I can generate 2 bi magic's with those 2 formulas. How do you generate more than that?

bobbym · 2010-05-25 03:06:19

Have you been able to generate more? As I understand it we can shift the rows of the sudoku amtrices and make new sudoku matrices. From that we can make more bi magics using the 2 simple formulas. But that is not the full Tarry - Cazalas method as Tarry who was a pretty good mathematician was able to generate tri magics also.

Thanks for the link by the way.

Ion · 2010-05-25 03:08:56

Separate both matrix as I say above in 2 square's A and B.
Take for example number 79 in Pfeffermann's incomplete square, 7+9=16=>1+6=7 and you got the B matrix value of 79.
Do the same with all the values and create the A matrix by your formula in the same order.
Tell me what you find intersting after you do that.

Ion · 2010-05-25 03:17:39

As far as i see Tarry-Cazalas method (wich i never read except the link i gave you) works on Pfeffermann's square and i find this very interesting.
If you got more about Tarry-Cazalas method please share with me.

bobbym · 2010-05-25 03:18:43

Hi;

Sorry, I am not seeing it. I can form the bimagic from A and B. But I don't understand what I am supposed to do with Pfeffermann's incomplete square.

chiquilla619 · 2010-05-27 13:12:46

Two runners finished a race in 80 seconds, another runner finished the race in 72 seconds, and the final runner finished in 68 seconds. The average of these times is ??

bobbym · 2010-05-27 13:16:06

Hi chiquilla619;

( 2 * 80 + 1 * 72 + 1 * 68 ) = 300. Now divide by 4 = 75

Math Is Fun Forum

#1 2010-05-23 21:31:47

How can I solve this problem?

#2 2010-05-23 21:38:11

Re: How can I solve this problem?

#3 2010-05-23 21:54:16

Re: How can I solve this problem?

#4 2010-05-23 21:59:37

Re: How can I solve this problem?

#5 2010-05-23 22:15:32

Re: How can I solve this problem?

#6 2010-05-23 22:17:48

Re: How can I solve this problem?

#7 2010-05-23 22:54:12

Re: How can I solve this problem?

#8 2010-05-23 23:05:11

Re: How can I solve this problem?

#9 2010-05-23 23:52:28

Re: How can I solve this problem?

#10 2010-05-23 23:56:21

Re: How can I solve this problem?

#11 2010-05-24 00:06:31

Re: How can I solve this problem?

#12 2010-05-24 00:23:18

Re: How can I solve this problem?

#13 2010-05-24 00:37:37

Re: How can I solve this problem?

#14 2010-05-24 00:41:43

Re: How can I solve this problem?

#15 2010-05-24 00:47:36

Re: How can I solve this problem?

#16 2010-05-25 01:42:12

Re: How can I solve this problem?

#17 2010-05-25 02:11:05

Re: How can I solve this problem?

#18 2010-05-25 02:25:59

Re: How can I solve this problem?

#19 2010-05-25 02:38:59

Re: How can I solve this problem?

#20 2010-05-25 03:06:19

Re: How can I solve this problem?

#21 2010-05-25 03:08:56

Re: How can I solve this problem?

#22 2010-05-25 03:17:39

Re: How can I solve this problem?

#23 2010-05-25 03:18:43

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#24 2010-05-27 13:12:46

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#25 2010-05-27 13:16:06

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