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

The Complementary Table Variation

A Loubere square

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.

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

Example in the order IC → IA → IB

  1. 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.
  2. Move down one cell, by taking the last number from the next line on the complementary table and placing this into the cell.
  3. Fill in the main right diagonal.
  4. Repeat the process with IA and IB until the square is filled, as shown below in squares 1-2.
IA
 
 
 
IB
 
 
 
 
IC
 
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
1531 5 28
21 304 27
2029 326
19352 25
34124 18
723 17 33
22 16 32 6
2 L7* 25 [1D](15,1,8)
441141 1531 5 28
104021 304 27 43
392029 326 49 9
19352 2548 8 38
34124 4714 37 18
72346 1336 17 33
224512 4216 32 6

Example in the order IC → IB → IA

  1. 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.
  2. Move down one cell, by taking the last number from the next line on the complementary table and placing this into the cell.
  3. Fill in the main right diagonal.
  4. Repeat the process with IC and IB until the square is filled, as shown below in squares 1-2.
IA
 
 
 
IB
 
 
 
 
IC
 
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
1531 12 28
21 3011 27
2029 1026
19359 25
34824 18
1423 17 33
22 16 32 13
2 L7* 25 [1D](15,8,1)
37448 1531 12 28
34721 3011 27 36
462029 1026 42 2
19359 2541 1 45
34824 407 44 18
142339 643 17 33
22385 4916 32 13

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
  1. 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.
  2. Move down one cell, by taking the last number from the next line on the complementary table and placing this into the cell.
  3. Fill in the main right diagonal.
  4. 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)
93920 293 47 28
381935 246 27 8
18341 4526 14 37
33744 2513 36 17
64324 1242 16 32
492311 4115 31 5
221040 2130 4 48
 
2 L7* 25 [1D](29,36,43)
164613 293 40 28
451235 239 27 15
11341 3826 21 44
33737 2520 43 10
63624 1949 9 32
422318 488 31 5
221747 1430 4 41
 
3 L7* 25 [1D](43,29,36)
23920 4310 33 28
381949 932 27 1
18488 3126 7 37
471430 256 36 17
132924 542 16 46
35234 4115 45 12
22340 2144 11 34
4 L7* 25 [1D](43,36,29)
16326 4310 40 28
45549 939 27 15
4488 3826 21 30
471437 2520 29 3
133624 1935 2 46
422318 341 45 12
221733 744 11 41
 
5 L7* 25 [1D](36,29,43)
24613 3617 33 28
451242 1632 27 1
114115 3126 7 44
402130 256 43 10
202924 549 9 39
35234 488 38 19
22347 1437 18 34
 
6 L7* 25 [1D](36,43,29)
9326 3617 47 28
31542 1646 27 8
44115 4526 14 30
402144 2513 29 3
204324 1235 2 39
492311 341 38 19
221033 737 18 48

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.


Copyright © 2008 by Eddie N Gutierrez. E-Mail: Fiboguti89@Yahoo.com