local solutions={}

function NQueen(q,r)
   if r==N+1 then
      local qsave={}
      for e=1,N do
         qsave[e]=q[e]
      end
      solutions[#solutions+1]=qsave
   else
      for j=1,N do
         valid=true
         for i=1,(r-1) do
            if ((q[i]==j or math.abs(q[i]-j)==math.abs(r-i)) and r>1) then
               valid=false
            end
         end
         if valid then
            q[r]=j
            NQueen(q,r+1)
         end
      end
   end
end

Dq={}
for i=1,N do
  Dq[i]=0
end

NQueen(Dq,1)
q=solutions[1]

-- on envoie tout à TeX
tex.print("Il y a "..#solutions.." solutions pour N="..N.."\\dots\\par")
tex.print("\\begin{tikzpicture}\\draw (0,0) grid ("..N..","..N..");")
for i=1,N do
   for j=1,N do
      if ((i%2 == 0) and (j%2==1)) or ((i%2 == 1) and (j%2==0))  then
         tex.print("\\fill[black!20] ("..(i-1)..","..(j-1)..") rectangle ("..i..","..j..");")
      end
      if q[j]==i then
         tex.print("\\node[scale=2] at("..(i-0.5)..","..(j-0.5)..") {\\wD};")
      end
   end
end

tex.print("\\end{tikzpicture}")