MagicSquare

Magic Square solver in Prolog

Introduction

The Magic Square is a simple mathematical puzzle whereby the numbers 1 to 9 must be placed on a 3x3 board such that each row, column and diagonal add up to 15.

So for example, given the following partial board...

 6 |   |   
---+---+---
   | 5 |   
---+---+---
 8 |   |   

...one possible solution is...

 6 | 7 | 2
---+---+---
 1 | 5 | 9
---+---+---
 8 | 3 | 4

...since summing the top row (6+7+2) is 15, summing the left-most column (6+1+8) is 15, and so on.

Running

The program was tested using on SWI-Prolog. To load the script:

?- consult('C:\\Users\\jdorr\\OneDrive\\Desktop\\Dev\\MagicSquare\\src\\magic_square.pl').

We can solve our example above with:

?- display_magic_square([[6,_,_],[_,5,_],[8,_,_]]).

 6 | 7 | 2
---+---+---
 1 | 5 | 9
---+---+---
 8 | 3 | 4
true;
false

We can also find all possible solutions for an empty board:

?- display_magic_square(X).

 2 | 7 | 6
---+---+---
 9 | 5 | 1
---+---+---
 4 | 3 | 8
X = [[2, 7, 6], [9, 5, 1], [4, 3, 8]] ;

 2 | 9 | 4
---+---+---
 7 | 5 | 3
---+---+---
 6 | 1 | 8
X = [[2, 9, 4], [7, 5, 3], [6, 1, 8]] ;

 4 | 3 | 8
---+---+---
 9 | 5 | 1
---+---+---
 2 | 7 | 6
X = [[4, 3, 8], [9, 5, 1], [2, 7, 6]] ;

 4 | 9 | 2
---+---+---
 3 | 5 | 7
---+---+---
 8 | 1 | 6
X = [[4, 9, 2], [3, 5, 7], [8, 1, 6]] ;

 6 | 1 | 8
---+---+---
 7 | 5 | 3
---+---+---
 2 | 9 | 4
X = [[6, 1, 8], [7, 5, 3], [2, 9, 4]] ;

 6 | 7 | 2
---+---+---
 1 | 5 | 9
---+---+---
 8 | 3 | 4
X = [[6, 7, 2], [1, 5, 9], [8, 3, 4]] ;

 8 | 1 | 6
---+---+---
 3 | 5 | 7
---+---+---
 4 | 9 | 2
X = [[8, 1, 6], [3, 5, 7], [4, 9, 2]] ;

 8 | 3 | 4
---+---+---
 1 | 5 | 9
---+---+---
 6 | 7 | 2
X = [[8, 3, 4], [1, 5, 9], [6, 7, 2]] ;
false.