Magic Squares Calculator (4 x 4)

[danmaz]

Hi guys

A magic square is a square filled with numbers (in this case 4x4 = 16) in such a way that you obtain the same
sum of numbers along any rows, columns or diagonals

As follows one of the simplest code on internet to generate 4x4 magic squares by filling it with numbers (from 1 to 16)

In total you will display all 880 combinations (excluded are rotations and mirror images).
A file is open for output , just to grasp all of them
Enjoy....comment are welcome

Daniele


' ******  MAGIC SQUARES 4x4 SOLVER  ****************

' *                                                *

' *  FREEWARE by danmaz                            *

' *  [e-mail]    www.molecularmodels.eu  *

' *                                                *

' **************************************************



' A magic square is a n times n square grid (where n is the number of cells on each side) filled with positive

' integers in the range 1 to n^2 such that each cell contains a different integer and the sum of the integers in each row

' column and diagonal is equal. This sum is called the magic constant or magic sum of the magic square.

' Here we generate the 880 magic squares of order 4 (magic sum is 34) discarding those obtained by reflections and rotations.



GLOBAL q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12, q13, q14, q15, q16, nTot

mainwin 64 24

 locate 10,4: print "+-----+-----+-----+-----+" '+-------------------+

 locate 10,5: print "| MAGIC SQUARE 4 X 4    |" '| q1 | q2 | q3 | q4 |

 locate 10,6: print "+-----+-----+-----+-----+" '+-------------------+

 locate 10,7: print "|    GENERATOR          |" '| q5 | q6 | q7 | q8 |

 locate 10,8: print "+-----+-----+-----+-----+" '+-------------------+

 locate 10,9: print "|     |     |     |     |" '| q9 | q10| q11| q12|

 locate 10,10:print "+-----+-----+-----+-----+" '+-------------------+

 locate 10,11:print "| << please wait ! >>   |" '| q13| q14| q15| q16|

 locate 10,12:print "+-----+-----+-----+-----+" '+-------------------+

 locate 4,16:print "magic square number = "

 locate 8,1:print "****  MAGIC SQUARES 4x4 SOLVER  ****"

 locate 14,2:print "Freeware by danmaz       JustBASIC v2.0"

 locate 4,18:print "Look at the complete output in MagicSquares.txt"

' q1....q16 are the actual values of each element of the square, as shown above

' s1....s16 are indeces that vary acoording to the variuos attemps to find q1...q16 values

' they refer to the position inside g16$....g1$

OPEN "MagicSquares.txt" for output as #1



FOR i = 1 TO 16:g16$ = g16$ + CHR$(i):NEXT i    ' start strig g16$ is generated in this line

nTot = 0   ' total number of squares is set to 0



' in the following 8 lines we impose some limits to the corner indeces

' in order to avoid magic squares obtained by rotation or mirroring of other existing

' q1 must be lowest value among (q1,q4,q13,q16), so cannot exceed 13



FOR s1 = 1 TO 13

FOR s4 = s1 + 1 TO 16

FOR s13 = s1 + 1 TO 16

FOR s16 = s1 + 1 TO 16

IF s1 = s4 OR s1 = s13 OR s1 = s16 OR s4 = s13 OR s4 = s16 OR s13 = s16 THEN 1000

IF s4 > s13 THEN 1000 ' il vertice q4 deve essere minore di q13

q1 = s1: q4 = s4: q13 = s13: q16 = s16

g12$ = ""



' here we produce g12$, which is then used to produce g11$...g10$... and so on

' it represents the elements still available (not present on the 4x4 square)

FOR i = 1 TO 16

  g1$ = MID$(g16$, i, 1)

  IF i = s1 OR i = s4 OR i = s13 OR i = s16 THEN 100

  g12$ = g12$ + g1$

100  NEXT i



' now we start the real job!

FOR s6 = 1 TO 12                               ' position 6 chosen by iterative cycle

  q6 = ASC(MID$(g12$, s6, 1))

  g11$ = LEFT$(g12$, s6 - 1) + MID$(g12$, s6 + 1)



  q11 = 34 - q1 - q6 - q16                     ' position 11 calculated

  IF q11 < 1 OR q11 > 16 THEN 980

  z = INSTR(g11$, CHR$(q11)): IF z = 0 THEN 980

  g10$ = LEFT$(g11$, z - 1) + MID$(g11$, z + 1)



FOR s10 = 1 TO 10                               ' position 10 chosen by iterative cycle

  q10 = ASC(MID$(g10$, s10, 1))

  g9$ = LEFT$(g10$, s10 - 1) + MID$(g10$, s10 + 1)



  q7 = 34 - q4 - q10 - q13                      ' position 7 calculated

  IF q7 < 1 OR q7 > 16 THEN 970

  z = INSTR(g9$, CHR$(q7)): IF z = 0 THEN 970

  g8$ = LEFT$(g9$, z - 1) + MID$(g9$, z + 1)



FOR s2 = 1 TO 8                                 ' position 2 chosen by iterative cycle

  q2 = ASC(MID$(g8$, s2, 1))

  g7$ = LEFT$(g8$, s2 - 1) + MID$(g8$, s2 + 1)



  q3 = 34 - q1 - q2 - q4                        ' position 3 calculated

  IF q3 < 1 OR q3 > 16 THEN 960

  z = INSTR(g7$, CHR$(q3)): IF z = 0 THEN 960

  g6$ = LEFT$(g7$, z - 1) + MID$(g7$, z + 1)



  q14 = 34 - q2 - q6 - q10                      ' position 14 calculated

  IF q14 < 1 OR q14 > 16 THEN 960

  z = INSTR(g6$, CHR$(q14)): IF z = 0 THEN 960

  g5$ = LEFT$(g6$, z - 1) + MID$(g6$, z + 1)



  q15 = 34 - q3 - q7 - q11                       ' position 15 calculated

  IF q15 < 1 OR q15 > 16 THEN 960

  z = INSTR(g5$, CHR$(q15)): IF z = 0 THEN 960

  g4$ = LEFT$(g5$, z - 1) + MID$(g5$, z + 1)



FOR s5 = 1 TO 4                                  ' position 5 chosen by iterative cycle

  q5 = ASC(MID$(g4$, s5, 1))

  g3$ = LEFT$(g4$, s5 - 1) + MID$(g4$, s5 + 1)



  q9 = 34 - q1 - q5 - q13                        ' position 9 calculated

  IF q9 < 1 OR q9 > 16 THEN 950

  z = INSTR(g3$, CHR$(q9)): IF z = 0 THEN 950

  g2$ = LEFT$(g3$, z - 1) + MID$(g3$, z + 1)



  q8 = 34 - q5 - q6 - q7                         ' position 8 calculated

  IF q8 < 1 OR q8 > 16 THEN 950

  z = INSTR(g2$, CHR$(q8)): IF z = 0 THEN 950

  g1$ = LEFT$(g2$, z - 1) + MID$(g2$, z + 1)



  q12 = 34 - q9 - q10 - q11                      ' position 12 calculated

  IF q12 < 1 OR q12 > 16 THEN 950

  IF ASC(g1$) <> q12 THEN 950

  if zc = 0 then call prepareTable:zc = zc + 1

  nTot = nTot + 1: LOCATE 28,16 : PRINT nTot;

  CALL writeIt   '  we reached a regular magic square, so we write it down

950 NEXT s5

960 NEXT s2

970 NEXT s10

980 NEXT s6

1000 NEXT s16:NEXT s13:NEXT s4:NEXT s1



PRINT " --> Job finished !! ":close #1

End



'-------------- sub's ----------------

Sub prepareTable

 locate 10,4: print "+-----+-----+-----+-----+"

 locate 10,5: print "|     |     |     |     |"

 locate 10,6: print "+-----+-----+-----+-----+"

 locate 10,7: print "|     |     |     |     |"

 locate 10,8: print "+-----+-----+-----+-----+"

 locate 10,9: print "|     |     |     |     |"

 locate 10,10:print "+-----+-----+-----+-----+"

 locate 10,11:print "|     |     |     |     |"

 locate 10,12:print "+-----+-----+-----+-----+"

End Sub



Sub writeIt

 locate 12,5:print q1;" ":locate 18,5:print q2;" ":locate 24,5:print q3;" ":locate 30,5:print q4;" "

 locate 12,7:print q5;" ":locate 18,7:print q6;" ":locate 24,7:print q7;" ":locate 30,7:print q8;" "

 locate 12,9:print q9;" ":locate 18,9:print q10;" ":locate 24,9:print q11;" ":locate 30,9:print q12;" "

 locate 12,11:print q13;" ":locate 18,11:print q14;" ":locate 24,11:print q15;" ":locate 30,11:print q16;" "

 print #1,"(";nTot;")"

 print #1,q1;"  ";q2;"  ";q3;"  ";q4

 print #1,q5;"  ";q6;"  ";q7;"  ";q8

 print #1,q9;"  ";q10;"  ";q11;"  ";q12

 print #1,q13;"  ";q14;"  ";q15;"  ";q16

 print #1,"-------------------"

End Sub