n:=9;;
L:=List([1..n],i->List([1..n],j->0));
pos_max:=0;

Backtracking:=function(i,j)
  local s,pos;

  # Print(L,"\n");

  for s in [1..n] do
    if(ForAny([1..i-1],i2->L[i2][j]=s)) then continue; fi;
    if(ForAny([1..j-1],j2->L[i][j2]=s)) then continue; fi;

    if(ForAny([1..i-1],k->L[((i-k-1) mod n) + 1][((j-k-1) mod n) + 1]=s)) then continue; fi;
    if(ForAny([1..i-1],k->L[((i-k-1) mod n) + 1][((j+k-1) mod n) + 1]=s)) then continue; fi;

    L[i][j] := s;

    pos:=n*i+j;
    if(pos>pos_max) then
      Print("Best thus far: ",L,"\n");
      pos_max := pos;
    fi;

    if(j=n) then
      if(i=n) then
        Print(L,"\n");
      else
        Backtracking(i+1,1);
      fi;
    else
      Backtracking(i,j+1);
    fi;

    L[i][j] := 0;
  od;
end;;

Backtracking(1,1);