1 | /* MAGIC, Magic Square */ |
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2 | |
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3 | /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */ |
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4 | |
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5 | /* In recreational mathematics, a magic square of order n is an |
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6 | arrangement of n^2 numbers, usually distinct integers, in a square, |
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7 | such that n numbers in all rows, all columns, and both diagonals sum |
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8 | to the same constant. A normal magic square contains the integers |
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9 | from 1 to n^2. |
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10 | |
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11 | (From Wikipedia, the free encyclopedia.) */ |
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12 | |
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13 | param n, integer, > 0, default 4; |
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14 | /* square order */ |
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15 | |
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16 | set N := 1..n^2; |
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17 | /* integers to be placed */ |
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18 | |
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19 | var x{i in 1..n, j in 1..n, k in N}, binary; |
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20 | /* x[i,j,k] = 1 means that cell (i,j) contains integer k */ |
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21 | |
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22 | s.t. a{i in 1..n, j in 1..n}: sum{k in N} x[i,j,k] = 1; |
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23 | /* each cell must be assigned exactly one integer */ |
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24 | |
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25 | s.t. b{k in N}: sum{i in 1..n, j in 1..n} x[i,j,k] = 1; |
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26 | /* each integer must be assigned exactly to one cell */ |
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27 | |
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28 | var s; |
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29 | /* the magic sum */ |
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30 | |
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31 | s.t. r{i in 1..n}: sum{j in 1..n, k in N} k * x[i,j,k] = s; |
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32 | /* the sum in each row must be the magic sum */ |
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33 | |
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34 | s.t. c{j in 1..n}: sum{i in 1..n, k in N} k * x[i,j,k] = s; |
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35 | /* the sum in each column must be the magic sum */ |
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36 | |
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37 | s.t. d: sum{i in 1..n, k in N} k * x[i,i,k] = s; |
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38 | /* the sum in the diagonal must be the magic sum */ |
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39 | |
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40 | s.t. e: sum{i in 1..n, k in N} k * x[i,n-i+1,k] = s; |
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41 | /* the sum in the co-diagonal must be the magic sum */ |
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42 | |
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43 | solve; |
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44 | |
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45 | printf "\n"; |
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46 | printf "Magic sum is %d\n", s; |
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47 | printf "\n"; |
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48 | for{i in 1..n} |
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49 | { printf{j in 1..n} "%3d", sum{k in N} k * x[i,j,k]; |
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50 | printf "\n"; |
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51 | } |
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52 | printf "\n"; |
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53 | |
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54 | end; |
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