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Magic Squares (4 x 4):

 Magic Squares 4 x 4, MC =  34, All  Diagonals Magic Squares 4 x 4, MC =  34, Main Diagonals Magic Squares 4 x 4, MC =  34, Associated

Magic Squares (5 x 5):

 Magic  Squares 5 x 5, MC = 65, a(25) = 1, 2, ... 25 Magic  Squares 5 x 5, MC = 65, Variables a(20) ... a(25) constant Magic  Squares 5 x 5, MC = 65, Diagonal  a( 1) ... a(25) constant Sudoku Squares 5 x 5, MC = 10, Pan Magic Sudoku Squares 5 x 5, MC = 10, Magic Sudoku Squares 5 x 5, MC = 10, Magic, Non Sudoku Diagonals Magic  Squares 5 x 5, MC = 65, Unique Base Squares Magic  Squares 5 x 5, MC = 65, Ultramagic Squares Magic  Squares 5 x 5, MC = 65, Associated Squares Magic  Squares 5 x 5, MC = 65, Concentric Squares (1) Magic  Squares 5 x 5, MC = 65, Concentric Squares (2) Magic  Squares 5 x 5, MC = 65, Eccentric  Squares (1) Magic  Squares 5 x 5, MC = 65, Eccentric  Squares (2) Magic  Squares 5 x 5, MC = 65, Diamond Inlay Magic  Squares 5 x 5, MC = 65, Diamond Inlay, Associated Magic  Squares 5 x 5, MC = 65, Diamond Inlay, Concentric Magic  Squares 5 x 5, MC = 65, Square Inlay Magic  Squares 5 x 5, MC = 65, Square and Diamond Inlay Magic  Squares 5 x 5, MC = 65, Rotation/Reflection Magic  Squares 5 x 5, MC = 65, Line Permutations Magic  Squares 5 x 5, MC = 65, Class {Aijk}

Magic Squares (6 x 6)
General:

 Magic Squares  6 x 6, MC = 111, Highlighted Variables Constant (1) Magic Squares  6 x 6, MC = 111, Highlighted Variables Constant (2) Magic Squares  6 x 6, MC = 111, Rotation/Reflection Magic Squares  6 x 6, MC = 111, Permutations lines n and (7 - n): Magic Squares  6 x 6, MC = 111, Permutations lines 1, 2, 3 and 4, 5, 6 Magic Squares  6 x 6, MC = 111, Combined Permutations Magic Squares  6 x 6, MC = 111, Symmetrical Diagonals (a) Magic Squares  6 x 6, MC = 111, Symmetrical Diagonals (b) Magic Squares  6 x 6, MC = 111, Class {Aijk} Symmetrical Diagonals Medjig Squares 3 x 3, MC = 9 Magic Squares  6 x 6, MC = 111, Deducted from Medjig Squares Medjig Squares 3 x 3, MC = 9  , Symmetrical Main Diagonals Magic Squares  6 x 6, MC = 111, Deducted from Medjig Squares Medjig Squares 3 x 3, MC = 9  , Almost Associated Magic Squares  6 x 6, MC = 111, Deducted from Medjig Squares Magic Squares  6 x 6, MC = 111, Concentric Squares (1) Magic Squares  6 x 6, MC = 111, Concentric Squares (2) Magic Squares  6 x 6, MC = 111, Concentric Squares (3) Magic Squares  6 x 6, MC = 111, Eccentric  Squares Magic Squares  6 x 6, MC = 111, Inlaid Magic Squares Magic Squares  6 x 6, MC = 111, Partly Rectangular Compact Magic Squares  6 x 6, MC = 111, Rectangular Compact Magic Squares  6 x 6, MC = 111, Rectangular Compact, Axial Symmetric Magic Squares  6 x 6, MC = 111, Axial Symmetric Magic Squares  6 x 6, MC = 111, Row Symmetric (Type 1) Magic Squares  6 x 6, MC = 111, Row Symmetric (Type 2) Magic Squares  6 x 6, MC = 111, Symmetric (Type 3) Magic Squares  6 x 6, MC = 111, Symmetric (Type 4) Magic Squares  6 x 6, MC = 111, Symmetric (Type 5) Magic Squares  6 x 6, MC = 111, Symmetric (Type 6) Magic Squares  6 x 6, MC = 111, Symmetric (Type 7) Magic Squares  6 x 6, MC = 111, Symmetric (Type 8) Magic Squares  6 x 6, MC = 111, Symmetric (Type 9) Magic Squares  6 x 6, MC = 111, Symmetric, Almost Associated Magic Squares  6 x 6, MC = 111, Symmetric, Square of the Sun Magic Squares  6 x 6, MC = 111, Bimagic Diagonals Magic Squares  6 x 6, MC = 111, Bimagic Columns

Magic Squares (6 x 6)
Non Consecutive Integers:

 Pan Magic Squares  6 x 6, MC = 150, Most Perfect Pan Magic Squares  6 x 6, MC = 150, 2 x 2 Compact, Class Example Pan Magic Squares  6 x 6, MC = 150, Associated Pan Magic Squares  6 x 6, MC = 120, Concentric, Associated Center Squares Pan Magic Squares  6 x 6, MC = 150, Compact Ultra Magic Pan Magic Squares  6 x 6, MC = 120, Pan Magic, Complete, Semi Mgc Sub Sqrs Pan Magic Squares  6 x 6, MC = 120, Associated, Semi Mgc Sub Sqrs Magic Squares  6 x 6, MC = 120, Rectangular Compact, Row Symmetric Magic Squares  6 x 6, MC = 120, Crosswise Symmetric Pan Magic Squares  6 x 6, MC = 120, Axial Symmetric Pan Magic Squares  6 x 6, MC = 126, Row Symmetric (Type 1) Pan Magic Squares  6 x 6, MC = 120, Row Symmetric (Type 2) Pan Magic Squares  6 x 6, MC = 120, Crosswise Symmetric Pan Magic Squares  6 x 6, MC = 120, Symmetric (Type 4) Partly Bimagic Squares  6 x 6, MC = 150, Bimagic Rows and Columns Partly Bimagic Squares  6 x 6, MC = 168, One Bimagic Diagonal Bimagic Squares  6 x 6, MC = 408, Associated Bimagic Squares  6 x 6, MC = 219, Crosswise Symmetric Bimagic Squares  6 x 6, MC = 330, Crosswise Symmetric

Magic Squares (7 x 7):

 Pan Magic Squares   7 x 7, MC = 175, b(i) - 1 =< a(i) =< b(i) + 1 Pan Magic Squares   7 x 7, MC = 175, Collection {Aijk} Sudoku Squares      7 x 7, MC =  21, Pan Magic Ultra Magic Squares 7 x 7, MC = 175, a(49) = 1, a(48) = 9, a(47) = 27 Ultra Magic Squares 7 x 7, MC = 175, Three Cell Patterns Sudoku Squares      7 x 7, MC =  21, Ultra Magic Ultra Magic Squares 7 x 7, MC = 175, Based on Attachment 7.4.3 Magic Squares       7 x 7, MC = 175, Concentric Squares (1) Magic Squares       7 x 7, MC = 175, Concentric Squares (2) Magic Squares       7 x 7, MC = 175, Eccentric  Squares (1) Magic Squares       7 x 7, MC = 175, Eccentric  Squares (2) Magic Squares       7 x 7, MC = 175, Overlapping Sub Squares (1) Magic Squares       7 x 7, MC = 175, Overlapping Sub Squares (2) Magic Squares       7 x 7, MC = 175, Overlapping Sub Squares (3) Magic Squares       7 x 7, MC = 175, Overlapping Sub Squares (4) Pan Magic Squares   5 x 5, MC = 125, Corner = 25 Magic Squares       7 x 7, MC = 175, Overlapping Sub Squares (6) Ass Magic Squares   7 x 7, MC = 175, Overlapping Sub Squares (7) Ass Magic Squares   7 x 7, MC = 175, Overlapping Sub Squares (8) Comp. Magic Squares 7 x 7, MC = 175, Ass Sub Squares (1) Comp. Magic Squares 7 x 7, MC = 175, Ass Sub Squares (2) Bordered Mgc Sqrs   7 x 7, MC = 175, Square and Diamond Inlay Ass Magic Squares   7 x 7, MC = 175, Diamond Inlays Order 3 and 4 Ass Magic Squares   7 x 7, MC = 175, Square  Inlays Order 3 and 4 Ultra Magic Squares 7 x 7, MC = 175, Conc Square and Square Inlay (1) Ultra Magic Squares 7 x 7, MC = 175, Conc Square and Square Inlay (2) Ultra Magic Squares 7 x 7, MC = 175, Square Inlays Ultra Magic Squares 7 x 7, MC = 175, Conc Square and Diamond Inlay Ultra Magic Squares 7 x 7, MC = 175, Square and Diamond Inlay (1) Ultra Magic Squares 7 x 7, MC = 175, Square and Diamond Inlay (2) Magic Squares       7 x 7, MC = 175, Bent Diagonals Magic Squares       7 x 7, MC = 175, Bent Diagonals, Symm Axes and Dia Pan Magic Squares   7 x 7, MC = 175, Bent Diagonals Pan Magic Squares   7 x 7, MC = 175, Bent Diagonals, Symm Axes and Dia Magic Squares       7 x 7, MC = 175, Bent Diagonals, Properties

Magic Squares (8 x 8):

 Pan Magic Squares 8 x 8, MC = 260, Class {Aijk} Pan Magic Squares 8 x 8, MC = 260, Collection {B} Pan Magic Squares 8 x 8, MC = 260, Collection {Aijk} based on Square 1 Pan Magic Squares 8 x 8, MC = 260, Unique Base Squares Pan Magic Squares 8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Magic Squares     8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Magic Squares     8 x 8, Composed of Magic Sub Squares (4 x 4) Pan Magic Squares 8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Containing Magic Middle Squares (4 x 4) Magic Squares     8 x 8, Composed of Magic Sub Squares (4 x 4) Containing Magic Middle Squares (4 x 4), Bent Diagonals Magic Squares     8 x 8, Composed of Associated Magic Sub Squares (4 x 4) Magic Squares     8 x 8, Composed of Associated Magic Sub Squares (4 x 4) Miscellaneous Valid Variable Ranges Magic Squares     8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Magic Squares     8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Miscellaneous Valid Variable Ranges Magic Squares     8 x 8, Composed of Magic Sub Squares (4 x 4) Magic Squares     8 x 8, Composed of Magic Sub Squares (4 x 4) Miscellaneous Valid Variable Ranges Magic Squares     8 x 8, Pan Magic Center Square (4 x 4) Magic Squares     8 x 8, Pan Magic Center Square (4 x 4) Miscellaneous Valid Variable Ranges Medjig Squares    4 x 4, MC =  12 Magic Squares     8 x 8, MC = 260, Deducted from Medjig Squares Magic Squares     8 x 8, MC = 260, Deducted from Medjig Squares Pan Magic Complete Squares Magic Squares     8 x 8, MC = 260, Deducted from Medjig Squares Associated Squares Franklin Squares  8 x 8, MC = 260, Main and Parallel Bent Diagonals Franklin Squares  8 x 8, MC = 260, a(64) = 17 and a(63) = 32 Franklin Squares  8 x 8, MC = 260, More Patterns summing to 260 Franklin Squares  8 x 8, MC = 260, a(64) = 17 and a(63) = 40 Barink Restrictions Pan Magic Squares 8 x 8, Franklin Properties 2 and 5 Pan Magic Squares 8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Franklin Property 5 Pan Magic Squares 8 x 8, Composed of Pan Magic Sub Squares (4 x 4) Franklin Properties 2 and 5, Barink Restrictions Pan Magic Squares 8 x 8, Most Perfect (Compact and Complete) Magic Squares     8 x 8, MC = 260, Concentric Squares (1) Magic Squares     8 x 8, MC = 260, Concentric Squares (2) Magic Squares     8 x 8, MC = 260, Eccentric Squares Magic Squares     8 x 8, MC = 260, Bordered Squares Ultra Mgc Sqrs    8 x 8, MC = 260, Compact Ultra Mgc Sqrs    8 x 8, MC = 260, Non Overlapping Sub Squares (a) Ultra Mgc Sqrs    8 x 8, MC = 260, Non Overlapping Sub Squares (b) Pan Magic Squares 8 x 8, MC = 260, Non Overl Sub Squares, Complete Ultra Mgc Sqrs    8 x 8, MC = 260, Rectangular Compact Pan Magic Squares 8 x 8, MC = 260, Rectangular Compact, Complete Magic Squares     8 x 8, MC = 260, Parttly Rect Compact, Associated Magic Squares     8 x 8, MC = 260, Parttly Rect Compact, Complete Magic Squares     8 x 8, MC = 260, Unique Inlaid Magic Squares Magic Squares     8 x 8, MC = 260, Composed of Magic Sub Squares Pan Magic Squares 4 x 4, MC = 130 Sudoku Squares    8 x 8, MC =  28 Quaternary Sqrs   Examples Quaternary Sqrs   8 x 8, MC =  12, Pan Magic, Associated Quaternary Sqrs   8 x 8, MC =  12, Pan Magic, Complete

Magic Squares (9 x 9):

 Pan Magic Squares 9 x 9, MC = 369, Class {Aijk} Pan Magic Squares 9 x 9, MC = 369, Collection {B} Pan Magic Squares 9 x 9, MC = 369, Collection {Aijk} based on Square 1 Pan Magic Squares 9 x 9, MC = 369, Unique Base Squares Compact Associated Pan Magic Squares, MC = 369 Compact Pan Magic Squares MC = 369 Every third-row and third-column summing to 123 Compact Associated Pan Magic Squares MC = 369 Every third-row and third-column summing to 123 Compact Associated Pan Magic Squares MC = 369, a(81) = 1 Every third-row and third-column summing to 123 Associated Magic Squares MC = 369, Misc Examples Every third-row and third-column summing to 123 Associated Magic Squares MC = 369, Misc Examples Regular Sub Squares summing to 369 Magic Squares     9 x 9, MC = 369, Concentric Squares (1) Magic Squares     9 x 9, MC = 369, Concentric Squares (2) Magic Squares     9 x 9, MC = 369, Bordered Squares Magic Squares     9 x 9, Eccentric Squares, Eccentric Corner Squares Magic Squares     9 x 9, Eccentric Squares, s1 = 369, s2 = 209 Base Squares for  9 x 9, Eccentric Squares, s1 = 369, s2 = 209 Magic Squares     9 x 9, Eccentric Squares, Overlapping Sub Squares Pan Magic Squares 9 x 9, Compact, Associated Sudoku Squares    9 x 9, MC = 36, Associated Compact Pan Magic Squares Every third-row and third-column summing to 12 Sudoku Squares    9 x 9, MC = 36, Associated Magic Squares Every third-row and third-column summing to 12 Sudoku Squares    9 x 9, MC = 36, Compact Associated Pan Magic Squares Sudoku Squares    9 x 9, MC = 36, Associated Magic Squares Regular Sub Squares Summing to 36 Ternary Squares   9 x 9, MC =  9, John Hendricks Sudoku Squares    9 x 9, MC = 36, John Hendricks Sudoku Squares    9 x 9, MC = 36, Non-Associated Compact Pan Magic Squares Ternary Squares   Examples Ternary Squares   9 x 9, MC =  9, Non-Associated Partly Compact Sudoku Squares    9 x 9, MC = 36, Non-Associated Partly Compact Ternary Squares   9 x 9, MC =  9, Compact Associated Pan Magic

Magic Squares (10 x 10):

 Medjig Squares     5 x  5, MC =   15 Magic Squares     10 x 10, MC =  505, Deducted from Medjig Squares Conc Mgc Sqrs     10 x 10, MC =  505, Deducted from Medjig Squares Ecc  Mgc Sqrs     10 x 10, MC =  505, Deducted from Medjig Squares Magic Squares     10 x 10, MC =  505, Deducted from Medjig Squares Magic Squares     10 x 10, MC =  505, Bimagic Diagonals Magic Squares     10 x 10, MC =  505, Bimagic Center Lines Magic Squares     10 x 10, MC =  505, Concentric Squares (1) Magic Squares     10 x 10, MC =  505, Concentric Squares (2) Magic Squares     10 x 10, MC =  505, Bordered Squares Magic Squares     10 x 10, Eccentric Squares, s1 = 505, s2 = 199 Magic Squares     10 x 10, Eccentric Squares, s1 = 505, s2 = 312 Composed Squares  10 x 10, MC =  505, Conc Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Ecc  Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Almost Ass Crnr Sqr Composed Squares  10 x 10, MC =  505, Almost Associated Composed Squares  10 x 10, MC =  505, Type 1, Conc Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Type 1, Ecc  Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Type 2, Conc Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Type 2, Ecc  Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Type 3, Ecc  Mgc Crnr Sqr Composed Squares  10 x 10, MC =  505, Type 4, Center Crosses Pan Magic Squares 10 x 10, MC = 2250, Most Perfect Ultra Mgc Sqrs    10 x 10, MC = 3510, Compact

Magic Squares (11 x 11):

 Magic Squares     11 x 11, MC =  671, Borders Magic Squares     11 x 11, MC =  671, Bordered Magic Squares     11 x 11, MC =  671, Eccentric Magic Squares     11 x 11, MC =  671, Composed Border Magic Squares     11 x 11, MC =  671, Associated, Composed (1) Magic Squares     11 x 11, MC =  671, Associated, Composed (2) Magic Squares     11 x 11, MC =  671, Associated, Composed (3) Magic Squares     11 x 11, MC =  671, Associated, Inlaid (1) Magic Squares     11 x 11, MC =  671, Associated, Inlaid (2) Magic Squares     11 x 11, MC =  671, Associated, Inlaid (3) Magic Squares     11 x 11, MC =  671, Composed, Overl Sub Sqrs (1) Magic Squares     11 x 11, MC =  671, Composed, Overl Sub Sqrs (2) Magic Squares     15 x 15, MC = 1695, Composed, Overl Sub Sqrs

Magic Squares (Higher Order):

 Barink Squares    12 x 12, MC =  870, a(144) = 72 and a(143) = 74 Morris Squares    12 x 12, MC =  870, a(136), a(138) ... a(140) and a(142) ... a(144) constant Morris Squares    12 x 12, MC =  870, Most Perfect (1) a(139) ... a(144) constant Magic  Squares    12 x 12, MC =  870, Most Perfect (2) a(143) ... a(144) constant Hendricks Squares  16 x 16, MC = 2056 Franklin  Squares  16 x 16, MC = 2056 (1) Franklin  Squares  16 x 16, MC = 2056 (2) Most Perfect Pan Magic Squares Franklin  Squares  16 x 16, MC = 2056 (3) Most Perfect Pan Magic Squares, Barink Restrictions

Interactive Solutions

 Pan Magic Squares   4 x  4, MC =   34, Binary Method Pan Magic Squares   5 x  5, MC =   65, Sudoku Method Magic Squares       6 x  6, MC =  111, Medjig Method Pan Magic Squares   7 x  7, MC =  175, Sudoku Method Most Perfect Msqrs  8 x  8, MC =  260, Binary Method Bimagic Squares     9 x  9, MC =  369, Ternary Method Most Perfect Msqrs 12 x 12, MC =  870, Basic Pattern Method Most Perfect Msqrs 16 x 16, MC = 2056, Basic Pattern Method