Office Applications and Entertainment, Magic Squares (Natural Numbers)

Contents

1.0 Introduction

2.0 Magic Squares (4 x 4)
2.1 Analytic Solution     Pan Magic Squares
2.2 Analytic Solution     Simple Magic Squares
2.3 Analytic Solution     Associated Magic Squares
2.4 Analytic Solution     Most Perfect Magic Squares
2.5 Other Magic Constants
2.7 Summary, Enumeration

3.0 Magic Squares (5 x 5)
3.1 Analytic Solution     Pan Magic Squares
3.2 Analytic Solution     Simple Magic Squares
3.3 Other Magic Constants
3.4 Rotation, Reflection, Row and Column Shifts
3.5 Transformations
3.6 Quinary Composition
5.4 Further Analysis      Symmetric Squares
5.5 Further Analysis      Concentric/Eccentric
5.6 Further Analysis      Qaudrant Magic Squares
5.7 Further Analysis      Miscellaneous Inlays
5.8 Summary, Enumeration

6.0  Magic Squares (6 x 6)
6.1  Analytic Solution     Pan Magic Squares (Don't Exist)
6.2  Analytic Solution     Simple Magic Squares
6.3  Transformations
6.4  Further Analysis      Symmetrical Main Diagonals
6.6  Further Analysis      Medjig Solutions
6.7  Further Analysis      Concentric/Eccentric/Inlaid
6.10 Further Analysis      Rectangular Compact
6.11 Further Analysis      Symmetries
6.9  Non Cons. Integers    Pan Magic, Part 1
6.12 Non Cons. Integers    Pan Magic, Part 2

7.0 Magic Squares (7 x 7)
7.1 Analytic Solution     Pan Magic Squares
7.2 Sudoku Comparable Method
7.3 Further Analysis      Ultra Magic Squares
7.5 Further Analysis      Concentric/Eccentric
7.6 Further Analysis      Miscellaneous Inlays
7.7 Further Analysis      Overlapping Sub Squares
7.8 Further Analysis      Non Overlapping Sub Squares
7.9 Further Analysis      Bent Diagonals

8.0 Magic Squares (8 x 8)
8.1 Pan Magic Squares     General
8.2 Magic Squares         Composed of Sub Squares
8.3 Medjig Solutions      Main Diagonals
8.4 Franklin Squares      Bent Diagonals
8.5 Pan Magic Squares     Based on Franklin Properties
8.6 Further Analysis      Miscellaneous Properties
8.7 More Solutions        Sudoku Comparable
8.8 Magic Squares         Concentric/Eccentric/Inlaid
8.9 Intermezzo

9.0 Magic Squares (9 x 9)
9.1 Analytic Solution     Pan Magic Squares
9.2 Further Analysis      Matrix Operation
9.4 Further Analysis      Compact/Symmetric
9.5 More Solutions        Sudoku Comparable
9.6 Magic Squares         Concentric/Eccentric
9.7 Magic Squares         Overlapping Sub Squares
9.7 Ass Mgc Squares       Miscellaneous Inlays
9.8 Analytic Solution     Quadrant Magic Squares
9.9 Intermezzo

10.0 Magic Squares (10 x 10)
10.1 Medjig Solutions     Main Diagonals
10.2 Magic Squares        Concentric/Eccentric/Inlaid
10.3 Magic Squares        Composed
10.4 Pan Magic Squares    Non Consecutive Integers
10.5 Further Analysis     Construction Methods

11.0 Magic Squares (11 x 11)
11.1 Magic Squares        Concentric/Eccentric
11.2 Magic Squares        Composed
11.3 Magic Squares        Associated

12.0 Magic Squares, Higher Order
12.1 Pan Magic Squares    12 x 12, Pan Magic Sub Squares
12.2 Pan Magic Squares    12 x 12, Franklin Like Properties
12.3 Franklin Squares     16 x 16, Bent Diagonals
12.4 Franklin Squares     16 x 16, Most Perfect Pan Magic Squares
12.5 Franklin Squares     16 x 16, Most Perfect/Barink Restrictions

12.6 Magic Squares        13 x 13, Overlapping Sub Squares
12.8 Magic Squares        13 x 13, Quadrant Magic Squares
12.9 Magic Squares        17 x 17, Quadrant Magic Squares

22.0 Magic Squares, Higher Order, Composed
22.1 4 x 4 Sub Squares    Magic Sums Identical
22.5 6 x 6 Sub Squares    Magic Sums Identical
23.0 Misc. Sub Squares    Magic Sums Different (1)
24.0 Misc. Sub Squares    Magic Sums Different (2)
25.1 Misc. Sub Squares    Overlapping (1)
25.7 Misc. Sub Squares    Overlapping (2)
26.0 Inlaid Squares       Associated Border
27.0 Inlaid Squares       Composed   Border (1)
28.0 Inlaid Squares       Composed   Border (2)
29.0 Single Even Order    Center Cross, Bordered

13.0 Construction of Single Magic Squares
13.1 Introduction
13.2 Pan Magic Squares    Odd
13.3 Magic Squares        Odd
13.4 Pan Magic Squares    Even

14.0 Special Squares, Prime Numbers

15.0 Special Squares, Bimagic Squares
15.1 Bimagic Squares (8 x 8) Part 1
15.3 Bimagic Squares (8 x 8) Part 2
15.2 Bimagic Squares (9 x 9) Part 1
15.4 Bimagic Squares (9 x 9) Part 2

15.7 Bimagic Squares (6 x 6)
15.8 Bimagic Squares (7 x 7)

15.9 Bimagic Squares (16 x 16)

16.0 Special Squares, Squares of Squares
16.1 Squares of Squares (3 x 3)
16.2 Squares of Squares (4 x 4)
16.3 Squares of Squares (5 x 5)
16.4 Squares of Squares (6 x 6)
16.5 Squares of Squares (7 x 7)

17.0 Special Squares, Two and Four Way V-ZigZag
17.2 V-Zigzag, Two Way (4 x 4)
17.3 V-Zigzag, Two Way (5 x 5)
17.4 V-Zigzag, Two and Four Way (6 x 6)
17.5 V-Zigzag, Two and Four Way (7 x 7)
17.6 V-Zigzag, Two and Four Way (8 x 8)

19.0 Special Squares, Bent Diagonals
19.2 Magic Squares (4 x 4)
19.3 Magic Squares (5 x 5)
19.4 Magic Squares (6 x 6)
19.4 Magic Squares (7 x 7)
19.4 Magic Squares (9 x 9)

18.0 Special Squares, Lozenge
18.2 Lozenge Squares (5 x 5)
18.3 Lozenge Squares (7 x 7)
18.4 Lozenge Squares (9 x 9)
18.5 Lozenge Squares (11 x 11)
18.4 Lozenge Squares (13 x 13)
18.5 Lozenge Squares (15 x 15)

List of VBA Subroutines
List of Spreadsheet Solutions
List of Attachments