#sudoku puzzle------------------------------------
param q;  # q = 2,3,4
param p := q*q;  # p = 4,9,16
 
set S:={1..p};
set T:={1..q};
var x{S,S,S} binary;  #=1 if cell (i,j) takes value k, (i,j,k) in SxSxS

minimize profit: 0;  # sudoku is just a feasibility problem

Sij{i in S,j in S}:sum{k in S}x[i,j,k]=1; 
Sik{i in S,k in S}:sum{j in S}x[i,j,k]=1;
Sjk{j in S,k in S}:sum{i in S}x[i,j,k]=1;
Tkmn{m in T,n in T,k in S}:sum{i in q*m-(q-1)..q*m,j in q*m-(q-1)..q*m}x[i,j,k]=1; 

data;
param q:=2;    # 4x4 grid with 2x2 subgrid 
#param q:=3;   # 9x9 grid with 3x3 subgrid

option solver cplex;
solve; display x;
for{i in S} {
   for{j in S}
      printf "%d ", sum{k in S} k*x[i,j,k];
   printf "\n";
}