puzzle problem

Question

Why magic square problem algorithm works ? 

Problem :- https://en.wikipedia.org/wiki/Magic_square

Any proof for the algorithm of problem why the algorithm works ?

Comments

Which algorithm ?

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I think he ask which algorithm followed by magic square, right @Kabir5454 ? & how it work

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Yes 👍 . And most importantly why it works ?

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Could you please redirect me to that algorithm ? If you mean constructing methods then which constructing method you are talking about ?

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https://www-geeksforgeeks-org.cdn.ampproject.org/v/s/www.geeksforgeeks.org/magic-square/amp/?amp_gsa=1&amp_js_v=a9&usqp=mq331AQKKAFQArABIIACAw%3D%3D#amp_tf=From%20%251%24s&aoh=16642830156529&referrer=https%3A%2F%2Fwww.google.com&ampshare=https%3A%2F%2Fwww.geeksforgeeks.org%2Fmagic-square%2F

@ankitgupta.1729 this one sir 

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@Kabir5454

Solution: https://www.overleaf.com/read/bgsdzvwrdpfz

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This diagonal sum is not equal to 65 and I did not the conversion how from rows and coloums we get this matrix as only first row and first column are fit with this 

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@Kabir5454 see this carefully 5*5 matrix format in magic square will be this and yes notice that diagonal element of every magic square will be continuous like here 11,12,13,14,15.

same for 3*3 diagonal will be 5,6,7

see this animated matrix carefully u will got the algorithm step

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@Kabir5454 actually i studied this magic square in class 9 & i remember some steps like every center value of magic square will be n^2+1/2 that is for 5*5 matrix center element will be =25+1=26/2=13 

and as rest element will be continuous in diagonal so put 11,12 & 14,15

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@Kabir5454 Please give some time to fix it. Since, rows and column sets are correct, so, in this case only 2 diagonal will create problem, and so, order of rows/columns needs to be fixed and conversion is not difficult, you just have to fix only one row and one column in any sequence and then for a particular set of column check which column element goes in which rows as you have already the row set.

@Nisha Bharti  question is not diagonal elements are in sequence, question is why it is so. So, you need to prove everything to justify it is so like centre element would be $S/n,$ Sum of two end diagonal elements is $\frac{2S}{n}$ etc. 

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@ankitgupta.1729 yes sir

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@ankitgupta.1729 sir yes the way you tried that is elegent please sir take your time and I will also try to by my own if got any thing I will add.

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@Kabir5454 can you please check that link again ? Let me know if you have any concerns.

Answer 1

I think there are more than one method to solving magic square ankit sir will clear this.

Comments

That's not the issue the problem is why this process works or any algorithm we know that there is a process but why that process works that is my doubt. Ankit Gupta sir solved almost the problem but still there is some portion should be fixed.