model sudoku
uses "mmxprs"; !gain access to the Xpress-Optimizer solver

!sample declarations section
declarations
s1 = 1..3
s2 = 4..6
s3 = 7..9
s = s1+s2+s3

x: array(s,s,s) of mpvar
end-declarations

costo := sum(i,j,k in s) 0*x(i,j,k)
forall(j,k in s) do
	sum(i in s) x(i,j,k) = 1
end-do

forall(i,k in s) do
	sum(j in s) x(i,j,k) = 1
end-do


forall(i,j in s) do
	sum(k in s) x(i,j,k) = 1
end-do

forall(k in s) do
	sum(i in s1,j in s1) x(i,j,k) = 1
	sum(i in s1,j in s2) x(i,j,k) = 1
	sum(i in s1,j in s3) x(i,j,k) = 1
	sum(i in s2,j in s1) x(i,j,k) = 1
	sum(i in s2,j in s2) x(i,j,k) = 1
	sum(i in s2,j in s3) x(i,j,k) = 1
	sum(i in s3,j in s1) x(i,j,k) = 1
	sum(i in s3,j in s2) x(i,j,k) = 1
	sum(i in s3,j in s3) x(i,j,k) = 1
end-do

forall(i,j,k in s) x(i,j,k) is_binary

x(1,1,8)=1
x(2,1,3)=1
x(3,1,4)=1
x(6,1,2)=1
x(8,1,1)=1
x(5,2,4)=1
x(2,3,7)=1
x(5,3,3)=1
x(2,4,8)=1
x(4,4,3)=1
x(6,4,7)=1
x(7,4,5)=1
x(9,4,6)=1
x(3,5,7)=1
x(4,5,5)=1
x(1,6,5)=1
x(5,6,8)=1
x(6,6,4)=1
x(7,7,4)=1
x(4,8,6)=1
x(5,8,1)=1
x(8,8,3)=1
x(3,9,1)=1
x(6,9,8)=1
x(7,9,7)=1




minimize(costo)
writeln("Begin running model")

forall(i,j,k in s) do
	if(getsol(x(i,j,k)))=1 then
		writeln(i,"",j,"",k," ",getsol(x(i,j,k)))
	end-if
end-do
writeln("End running model")

end-model