Add magic-square exercise

config.json

@@ -901,6 +901,14 @@
         "practices": [],
         "prerequisites": [],
         "difficulty": 1
+      },
+      {
+        "slug": "magic-square",
+        "name": "Magic Square",
+        "uuid": "0dabf6ec-98fb-442c-9e1f-684108a67f26",
+        "practices": [],
+        "prerequisites": [],
+        "difficulty": 1
       }
     ],
     "foregone": [

exercises/practice/magic-square/.docs/instructions.md

@@ -0,0 +1,14 @@
+# Instructions
+
+Your task is to, given a square of positive integers, determine if the square is a magic square.
+A magic square is one where the sum of the numbers in each row, column and both diagonals are the same.
+
+As an example, consider the following square:
+
+```text
+4 9 2
+3 5 7
+8 1 6
+```
+
+This is a magic square, as the sum of every row, column and both diagonals is equal to 15.

exercises/practice/magic-square/.meta/config.json

@@ -0,0 +1,17 @@
+{
+  "authors": [
+    "erikschierboom"
+  ],
+  "files": {
+    "solution": [
+      "magic_square.pl"
+    ],
+    "test": [
+      "magic_square_tests.plt"
+    ],
+    "example": [
+      ".meta/magic_square.example.pl"
+    ]
+  },
+  "blurb": "Check if a square is a magic square"
+}

exercises/practice/magic-square/.meta/magic_square.example.pl

@@ -0,0 +1,23 @@
+:- use_module(library(clpfd)).
+
+diagonals(Rows, LeftRightDiagonal, RightLeftDiagonal) :-
+    length(Rows, N),
+    numlist(1, N, Indices),
+    reverse(Indices, ReverseIndices),
+    pairs_keys_values(LeftRightIndices, Indices, Indices),    
+    pairs_keys_values(RightLeftIndices, ReverseIndices, Indices),
+    maplist(diagonal_element(Rows), LeftRightIndices, LeftRightDiagonal),
+    maplist(diagonal_element(Rows), RightLeftIndices, RightLeftDiagonal).
+
+diagonal_element(Rows, X-Y, Value) :- nth1(Y, Rows, Row), nth1(X, Row, Value).
+
+magic_square(Rows) :-
+    maplist(sumlist, Rows, RowSums),
+    transpose(Rows, Cols),
+    maplist(sumlist, Cols, ColSums),
+    diagonals(Rows, LeftRightDiagonal, RightLeftDiagonal),
+    sumlist(LeftRightDiagonal, LeftRightDiagonalSum),
+    sumlist(RightLeftDiagonal, RightLeftDiagonalSum),
+    append([RowSums, ColSums, [LeftRightDiagonalSum, RightLeftDiagonalSum]], Sums),
+    sort(Sums, SortedSums),
+    length(SortedSums, 1).

exercises/practice/magic-square/magic_square.pl

@@ -0,0 +1 @@
+magic_square(Rows).

exercises/practice/magic-square/magic_square_tests.plt

@@ -0,0 +1,52 @@
+pending :-
+    current_prolog_flag(argv, ['--all'|_]).
+pending :-
+    write('\nA TEST IS PENDING!\n'),
+    fail.
+
+:- begin_tests(magic_square).
+
+    test(magic_square_order_3, condition(true)) :-
+        Square = 
+            [
+                [2, 7, 6],
+                [9, 5, 1],
+                [4, 3, 8]
+            ],
+        magic_square(Square).
+
+    test(magic_square_order_4, condition(pending)) :-
+        Square = 
+            [
+                [ 2, 16, 13,  3],
+                [11,  5,  8, 10],
+                [ 7,  9, 12,  6],
+                [14,  4,  1, 15]
+            ],
+        magic_square(Square).
+
+    test(magic_square_order_9, condition(pending)) :-
+        Square = 
+            [
+                [31, 76, 13, 36, 81, 18, 29, 74, 11],
+                [22, 40, 58, 27, 45, 63, 20, 38, 56],
+                [67,  4, 49, 72,  9, 54, 65,  2, 47],
+                [30, 75, 12, 32, 77, 14, 34, 79, 16],
+                [21, 39, 57, 23, 41, 59, 25, 43, 61],
+                [66,  3, 48, 68,  5, 50, 70,  7, 52],
+                [35, 80, 17, 28, 73, 10, 33, 78, 15],
+                [26, 44, 62, 19, 37, 55, 24, 42, 60],
+                [71,  8, 53, 64,  1, 46, 69,  6, 51]
+            ],
+        magic_square(Square).
+
+    test(invalid_magic_square, [fail, condition(pending)]) :-
+        Square = 
+            [
+                [1, 2, 3],
+                [4, 5, 6],
+                [7, 8, 9]
+            ],
+        magic_square(Square).
+
+:- end_tests(magic_square).