New Loubère Magic Square Method-7x7 Squares (Part IIIB)

The Complementary Table Variation

Continuation from Part IIIA

This page is a continuation of New Loubère Magic Square Method (Part IIIA). Again the nomenclature of the Loubère squares is Ln^* (center cell#)[1D](n1,n2,n3) where (Ln^* signifies a nxn Loubère square with center cell number and a break followed by 1 move Down. The complementary table is composed of three groups A, B and C a total of six squares are possible with the numbers n1,n2 and n3 in any of six combinations.

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Examples of Magic 7x7 Squares Using the Loubère[1D] Method

Example in the order IC → IA → IB

Place the first number of IC at the center of the first row of a 7x7 square (the regular historical square) and fill in cells by advancing diagonally upwards to the right until blocked by a previous number.
Move down one cell, by taking the last number from the next line on the complementary table and placing this into the cell.
Fill in the main right diagonal.
Repeat the process with IA and IB until the square is filled, as shown below in squares 1-2.

1	2	3	4	5	6	7
49	48	47	46	45	44	43

8	9	10	11	12	13	14
							22	23	24
										25
							28	27	26
42	41	40	39	38	37	36

15	16	17	18	19	20	21
35	34	33	32	31	30	29

1
			15	31	5	28
		21	30	4	27
	20	29	3	26
19	35	2	25
34	1	24				18
7	23				17	33
22				16	32	6

⇒

2 L7^* 25 [1D](15,1,8)
44	11	41	15	31	5	28
10	40	21	30	4	27	43
39	20	29	3	26	49	9
19	35	2	25	48	8	38
34	1	24	47	14	37	18
7	23	46	13	36	17	33
22	45	12	42	16	32	6

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Example in the order IC → IB → IA

Place the first number of IA at the center of the first row of a 7x7 square and fill in cells by advancing diagonally upwards to the right until blocked by a previous number.
Move down one cell, by taking the last number from the next line on the complementary table and placing this into the cell.
Fill in the main right diagonal.
Repeat the process with IC and IB until the square is filled, as shown below in squares 1-2.

1	2	3	4	5	6	7
49	48	47	46	45	44	43

8	9	10	11	12	13	14
							22	23	24
										25
							28	27	26
42	41	40	39	38	37	36

15	16	17	18	19	20	21
35	34	33	32	31	30	29

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

⇒

2 L7^* 25 [1D](15,8,1)
37	4	48	15	31	12	28
3	47	21	30	11	27	36
46	20	29	10	26	42	2
19	35	9	25	41	1	45
34	8	24	40	7	44	18
14	23	39	6	43	17	33
22	38	5	49	16	32	13

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Six Examples of IIA, IIB and IIC

To complete the last six examples the right hand complementary table from Part IIIA (shown below) is used in generating these squares:

IIA

IIB

IIC

29	30	31	32	33	34	35
7	6	5	4	3	2	1

43	44	45	46	47	48	49
							22	23	24
										25
							28	27	26
14	13	12	11	10	9	8

36	37	38	39	40	41	42
21	20	19	18	17	16	15

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Place the first number of either IIA, IIB or IIC at the center of the first row of a 7x7 square and fill in cells by advancing diagonally upwards to the right until blocked by a previous number.
Move down one cell, by taking the last number from the next line on the complementary table and placing this into the cell.
Fill in the main right diagonal.
Repeat the process with either IIA, IIB or IIC until the square is filled, as shown below in squares 1-6.

1 L7^* 25 [1D](29,43,36)
9	39	20	29	3	47	28
38	19	35	2	46	27	8
18	34	1	45	26	14	37
33	7	44	25	13	36	17
6	43	24	12	42	16	32
49	23	11	41	15	31	5
22	10	40	21	30	4	48

2 L7^* 25 [1D](29,36,43)
16	46	13	29	3	40	28
45	12	35	2	39	27	15
11	34	1	38	26	21	44
33	7	37	25	20	43	10
6	36	24	19	49	9	32
42	23	18	48	8	31	5
22	17	47	14	30	4	41

3 L7^* 25 [1D](43,29,36)
2	39	20	43	10	33	28
38	19	49	9	32	27	1
18	48	8	31	26	7	37
47	14	30	25	6	36	17
13	29	24	5	42	16	46
35	23	4	41	15	45	12
22	3	40	21	44	11	34

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4 L7^* 25 [1D](43,36,29)
16	32	6	43	10	40	28
45	5	49	9	39	27	15
4	48	8	38	26	21	30
47	14	37	25	20	29	3
13	36	24	19	35	2	46
42	23	18	34	1	45	12
22	17	33	7	44	11	41

5 L7^* 25 [1D](36,29,43)
2	46	13	36	17	33	28
45	12	42	16	32	27	1
11	41	15	31	26	7	44
40	21	30	25	6	43	10
20	29	24	5	49	9	39
35	23	4	48	8	38	19
22	3	47	14	37	18	34

6 L7^* 25 [1D](36,43,29)
9	32	6	36	17	47	28
31	5	42	16	46	27	8
4	41	15	45	26	14	30
40	21	44	25	13	29	3
20	43	24	12	35	2	39
49	23	11	34	1	38	19
22	10	33	7	37	18	48

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This completes this section on New Loubère Magic Square Method (Part IIIB). To see a new Loubère Two Step Magic Square Method (Part I). To return to homepage.