thanks, Geo, 64-square matrix, r u a matrix geek?

Ha Rony

Yes a 64-square Matrix Arithmetic! Watch out for it!

And, yes! In the good sense of the word 'geek', but not otherwise. He he!

Cheers!

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Excuse me, Geoette; what is universal method? What are the rest of the methods? Mind sharing them with us?

Hello Lady

There are many ways to construct magic squares, but the standard and most simple way is to follow certain configurations which generate regular patterns. Magic squares exist for all values of n, with only one exception - it is impossible to construct a magic square of order 2, i.e 4 squares. Magic squares can be classified into three types: odd, doubly even (n divisible by four) and singly even (n even, but not divisible by four). Odd and doubly even magic squares are easy to generate; the construction of singly even magic squares is more difficult but several methods exist. My impending 64-square is one such example.

The universal method of constructing an odd order magical square is to start from the central column of the first row with the number 1, the fundamental movement for filling the squares is diagonally up and right, one step at a time. If a filled square is encountered, one moves vertically down one square instead, then continuing as before. When a move would leave the square, it is wrapped around to the last row or first column, respectively.
Similar patterns can also be obtained by starting from other squares.

Another method of construction of an odd order magical square is to use the downward diagonal slide, which I have designed myself. It is complicated and more time consuming, yet difficult to explain. Spare me!

For even order magical square, go left to right through the square filling counting and filling in on the diagonals only. Then continue by going left to right from the top left of the table and fill in counting down from 16 or n²as shown below.

01 -- -- 04
-- 06 07 --
-- 10 11 --
13 -- -- 16

01 15 14 04
12 06 07 09
08 10 11 05
13 03 02 16

May I refer you to the term "magical square" found in the CENTURY global-language dictionary, Volume Five, Page 16. There you will find a solution to magical square order 4 employing the universal method; almost similar to your solution except that you used the downward method instead of the horizontal method. Which is why I guess you are left-handed, as a left handed person (I think) finds it more versatile to write downwards than horizontally.

I hope I have made myself understood. And after having said all these, I wonder if I should continue with Matrix Arithmetic anymore!

Below is a link for better understanding on how magical squares are being constructed.

Looks like it's 'sayonara' to Magical Square from here!

Cheers all!


http://mathworld.wolfram.com/MagicSquare.html

Thank you for sharing, Geoette.

(And, for your information, I'm not a left-hander. The reason why my way of presenting the numbers is different from yours is because I'm using another method, that is, by calculating.)

Btw, do continue with your 64-square matrix arithmatic game --- Rony loves it so much! Guess others think likewise.

Hi Lady

Okay! I will design a 64-square Matrix; one which could be easy to solve without stipulating the numerals to be used. Also, I will be looking for an alternate solution that requires participants to use a specific series of numerals.

Until then, ciao and many thanks for your interest in this thread.

Hello All Members & Viewers

Here it comes as promised!

Construct an 8 by 8 (64-square) diagram with all the columns, rows and the two diagonal lines, each having a constant of 924.

There's no restriction on the numerals to be used.

Easy! Right?

Good Luck to all!

ps: Shall we "bar" Lady Futari from participation until the next round when I will specify the series of numerals to be used?

No hard feelings, Lady It's just too easy for you!

it's easy to get an answer by cheating from the previous
4 by 4 matrix. i dont wanna cheat, but seems it's my only gift to cheat, sucks

123 109 110 120 123 109 110 120
112 118 117 115 112 118 117 115
116 114 113 119 116 114 113 119
111 121 122 108 111 121 122 108
123 109 110 120 123 109 110 120
112 118 117 115 112 118 117 115
116 114 113 119 116 114 113 119
111 121 122 108 111 121 122 108

Geo, please dont count this as an answer, i just let you know sometimes ppl can get an answer by cheating

Yes, Geo, u should bar Futari from this game

Well done, Rony.

Strictly speaking, magical squares should not comprise of repeated numerals, otherwise the impossible Order 2 (4 squares) becomes possible by using four 1's or four 2's and so on.

You have used four times each of 108~123 (inclusive) in the 64 squares. I can't say it is wrong as I did say that the solution does not restrict participants the free use of numerals. It was my mistake!

In any case, would you like to give it another attempt; this time with no repeated numerals.

I will place on record that you have solved a 64 Magaical Square riddle this day. Congratulations!

Cheers!

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Deal! This is exactly what I have in mind.