g.van.uden@tip.nl wrote:

Date: Sat, 16 Aug 1997

Hi Shin, (is that your first name?)

I read your posting in rec.puzzles and brought a visit to your site. You said you looked for books which handled magic squares. I have a Puzzle site and did a item on magic squares, but not as detailed as yours.
When doing research for good puzzles, I stumbled on a puzzle book. One chapter handled the magic squares and regular orders of the 6th, 10th, 14th were explained, as well as the easier odd orders.
A guy named Strachney thought of a method to construct them. There was no background on him.
Also a Frenchman named Phillippe de la Hire, and Benjamin Franklin are mentioned as inventors of ways to construct different orders.
The book was in Dutch by Pieter van Delft & Jack Botermans and was called "Spelen met Puzzels" which translates in "Playing with Puzzles".
The Strachney method seemed easier to comprehend then your method, explained on your site. I remember that the Strachney method involved a lot of number switching as well. But I can't recall how it actually was done.
If you want I can find it again in the library and send you the method he used.

Hope these names helps you to learn more about de history of magic squares Have a great day,

Cheerio, GijsjebertiX
Holand
http://www.tip.nl/users/g.van.uden/index.htm
E-mail: g.van.uden@tip.nl

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/ /_  \\|  || \__ \ | |  __/ |_)  |  __/ |  | |  |  |  | /   \
\____/|_|/ |___// |\___ |___/ \___|_| \_\  |_|/_/\_\
          |__/    |__/

Date: Tue, 19 Aug 1997

Hi Kwon,

GijsjebertiX is my first name, cheerio is a typically English collogilism, meaning "good wishes - goodbey".

The strachey methodfor a magic square order 6:

Devide a square of 6 by 6 into four smaller squares of 3 by 3 (fig1). Start in the upper left square with entering the numbers 1 to 9 according the Lo-Shu method. Go on in the lower right square with entering the number 10 to 18. Write the 10 in the same cel which corresponds with the same cel where 1 is placed, and so on. Then proceed with the upper right square. Here you write the numbers 19 to 27. I9 corresponding with cel 1 and so on.
Finally the lower left square. Enter the numbers 28 to 36 in the same way as you did earlier.

Now we start the swiching:

In the figures I attached you should be able to see the switching metod.
For in the book it's all in Dutch and I not that good in translating the techno-babble.
Try and find this methods in English I sure it out there if you look for it.

If you didn't get the attachment let me know I will send it another way.

8 1 6 26 19 24

3 5 7 21 23 25

4 9 2 22 27 20

35 28 33 17 10 15

30 32 34 12 14 16

31 36 29 13 18 11

fig. 1

35	1	6	26	19	24
3	32	7	21	23	25
31	9	2	22	27	20
8	28	33	17	10	15
30	5	34	12	14	16
4	36	29	13	18	11

The gray cells are switched with the yellow ones

17	24	1	8	15	67	74	51	58	65
23	5	7	14	16	73	55	57	64	66
4	6	13	20	22	54	56	63	70	72
10	12	19	21	3	60	62	69	71	53
11	18	25	2	9	61	68	75	52	59
92	99	76	83	90	42	49	26	33	40
98	80	82	89	91	48	30	32	39	41
79	81	88	95	97	29	31	38	45	47
85	87	94	96	78	35	37	44	46	28
86	93	100	77	84	36	43	50	27	34

fig. 3

92	99	1	8	15	67	74	51	58	40
98	80	7	14	16	73	55	57	64	41
4	81	88	20	22	54	56	63	70	47
85	87	19	21	3	60	62	69	71	28
86	93	25	2	9	61	68	75	52	34
17	24	76	83	90	42	49	26	33	65
23	5	82	89	91	48	30	32	39	66
79	6	13	95	97	29	31	38	45	72
10	12	94	96	78	35	37	44	46	53
11	18	100	77	84	36	43	50	27	59

order 14 switching scheme

�

Cheerio, GijsjebertiX

http://www.tip.nl/users/g.van.uden/index.htm
E-mail: g.van.uden@tip.nl

   ___ _  _       _        _                 _    ___   __
  / _   (_)(_)__ (_) ___| |_    __    __| |_ (_)   \/  /
 / /_  \/  || / __| | |/ _ \ '_  \  / _ \  /__| __| |  \   /
/ /_  \\|  || \__ \ | |  __/ |_)  |  __/ |  | |  |  |  | /   \
\____/|_|/ |___// |\___ |___/ \___|_| \_\  |_|/_/\_\
         |__/    |__/

8	1	6	26	19	24
3	5	7	21	23	25
4	9	2	22	27	20
35	28	33	17	10	15
30	32	34	12	14	16
31	36	29	13	18	11

35	1	6	26	19	24
3	32	7	21	23	25
31	9	2	22	27	20
8	28	33	17	10	15
30	5	34	12	14	16
4	36	29	13	18	11

17	24	1	8	15	67	74	51	58	65
23	5	7	14	16	73	55	57	64	66
4	6	13	20	22	54	56	63	70	72
10	12	19	21	3	60	62	69	71	53
11	18	25	2	9	61	68	75	52	59
92	99	76	83	90	42	49	26	33	40
98	80	82	89	91	48	30	32	39	41
79	81	88	95	97	29	31	38	45	47
85	87	94	96	78	35	37	44	46	28
86	93	100	77	84	36	43	50	27	34

92	99	1	8	15	67	74	51	58	40
98	80	7	14	16	73	55	57	64	41
4	81	88	20	22	54	56	63	70	47
85	87	19	21	3	60	62	69	71	28
86	93	25	2	9	61	68	75	52	34
17	24	76	83	90	42	49	26	33	65
23	5	82	89	91	48	30	32	39	66
79	6	13	95	97	29	31	38	45	72
10	12	94	96	78	35	37	44	46	53
11	18	100	77	84	36	43	50	27	59

8	1	6	26	19	24
3	5	7	21	23	25
4	9	2	22	27	20
35	28	33	17	10	15
30	32	34	12	14	16
31	36	29	13	18	11

35	1	6	26	19	24
3	32	7	21	23	25
31	9	2	22	27	20
8	28	33	17	10	15
30	5	34	12	14	16
4	36	29	13	18	11

17	24	1	8	15	67	74	51	58	65
23	5	7	14	16	73	55	57	64	66
4	6	13	20	22	54	56	63	70	72
10	12	19	21	3	60	62	69	71	53
11	18	25	2	9	61	68	75	52	59
92	99	76	83	90	42	49	26	33	40
98	80	82	89	91	48	30	32	39	41
79	81	88	95	97	29	31	38	45	47
85	87	94	96	78	35	37	44	46	28
86	93	100	77	84	36	43	50	27	34

92	99	1	8	15	67	74	51	58	40
98	80	7	14	16	73	55	57	64	41
4	81	88	20	22	54	56	63	70	47
85	87	19	21	3	60	62	69	71	28
86	93	25	2	9	61	68	75	52	34
17	24	76	83	90	42	49	26	33	65
23	5	82	89	91	48	30	32	39	66
79	6	13	95	97	29	31	38	45	72
10	12	94	96	78	35	37	44	46	53
11	18	100	77	84	36	43	50	27	59

8	1	6	26	19	24
3	5	7	21	23	25
4	9	2	22	27	20
35	28	33	17	10	15
30	32	34	12	14	16
31	36	29	13	18	11

35	1	6	26	19	24
3	32	7	21	23	25
31	9	2	22	27	20
8	28	33	17	10	15
30	5	34	12	14	16
4	36	29	13	18	11

17	24	1	8	15	67	74	51	58	65
23	5	7	14	16	73	55	57	64	66
4	6	13	20	22	54	56	63	70	72
10	12	19	21	3	60	62	69	71	53
11	18	25	2	9	61	68	75	52	59
92	99	76	83	90	42	49	26	33	40
98	80	82	89	91	48	30	32	39	41
79	81	88	95	97	29	31	38	45	47
85	87	94	96	78	35	37	44	46	28
86	93	100	77	84	36	43	50	27	34

92	99	1	8	15	67	74	51	58	40
98	80	7	14	16	73	55	57	64	41
4	81	88	20	22	54	56	63	70	47
85	87	19	21	3	60	62	69	71	28
86	93	25	2	9	61	68	75	52	34
17	24	76	83	90	42	49	26	33	65
23	5	82	89	91	48	30	32	39	66
79	6	13	95	97	29	31	38	45	72
10	12	94	96	78	35	37	44	46	53
11	18	100	77	84	36	43	50	27	59