/usr/share/doc/glpk-utils/examples/numbrix.mod is in glpk-utils 4.65-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | /* Numbrix, Number Placement Puzzle */
/* Written in GNU MathProg by Robert Wood <rwood@targus.com> */
/* Numbrix is a logic-based number-placement puzzle.[1]
* The objective is to fill the grid so that each cell contains
* digits in sequential order taking a horizontal or vertical
* path; diagonal paths are not allowed. The puzzle setter
* provides a grid often with the outer most cells completed.
*
* Completed Numbrix puzzles are usually a square of numbers
* in order from 1 to 64 (8x8 grid) or from 1 to 81 (9x9 grid),
* following a continuous path in sequence.
*
* The modern puzzle was invented by Marilyn vos Savant in 2008
* and published by Parade Magazine under the name "Numbrix",
* near her weekly Ask Marilyn article.
*
* http://en.wikipedia.org/wiki/Numbrix */
set I := {1..9};
set J := {1..9};
set VALS := {1..81};
param givens{I, J}, integer, >= 0, <= 81, default 0;
/* the "givens" */
param neighbors{i in I,j in J, i2 in I, j2 in J} , binary :=
(if abs(i - i2) + abs(j -j2) == 1 then
1
else
0
);
/* defines which spots are the boards are neighbors */
var x{i in I, j in J, k in VALS}, binary;
/* x[i,j,k] = 1 means cell [i,j] is assigned number k */
s.t. fa{i in I, j in J, k in VALS: givens[i,j] != 0}:
x[i,j,k] = (if givens[i,j] = k then 1 else 0);
/* assign pre-defined numbers using the "givens" */
s.t. fb{i in I, j in J}: sum{k in VALS} x[i,j,k] = 1;
/* each cell must be assigned exactly one number */
s.t. singleNum {k in VALS}: sum{i in I, j in J} x[i,j,k] = 1;
/* a value can only occur once */
s.t. neighborContraint {i in I, j in J, k in 1..80}:
x[i,j,k] <= sum{i2 in I, j2 in J} x[i2,j2,k+1] * neighbors[i,j,i2,j2];
/* each cell must have a neighbor with the next higher value */
/* there is no need for an objective function here */
solve;
for {i in I}
{ for {0..0: i = 1 or i = 4 or i = 7}
printf " +----------+----------+----------+\n";
for {j in J}
{ for {0..0: j = 1 or j = 4 or j = 7} printf(" |");
printf " %2d", sum{k in VALS} x[i,j,k] * k;
for {0..0: j = 9} printf(" |\n");
}
for {0..0: i = 9}
printf " +----------+----------+----------+\n";
}
data;
param givens : 1 2 3 4 5 6 7 8 9 :=
1 . . . . . . . . .
2 . 11 12 15 18 21 62 61 .
3 . 6 . . . . . 60 .
4 . 33 . . . . . 57 .
5 . 32 . . . . . 56 .
6 . 37 . . . . . 73 .
7 . 38 . . . . . 72 .
8 . 43 44 47 48 51 76 77 .
9 . . . . . . . . . ;
end;
|