sudoku.lua

local field = {}

for i = 1, 9 do
  local buf = io.read()
  field[i] = {}
  for j = 1, 9 do
    field[i][j] = tonumber(buf:sub(j, j))
  end
end

local function print_field(field)
  for i = 1, 9 do
    for j = 1, 9 do
      if field[i][j] == nil then
        io.write(". ")
      else
        io.write(tostring(field[i][j]) .. " ")
      end
      if j % 3 == 0 then
        if j ~= 9 then
          io.write("| ")
        else
          io.write("\n")
        end
      end
    end
    if i % 3 == 0 and i ~= 9 then
      io.write(("-"):rep(6).."+"..("-"):rep(7).."+"..("-"):rep(6).."\n")
    end
  end
end

function solve(field, xi, yi)
  xi = xi or 1
  yi = yi or 1
  if yi > 9 then
    return true
  elseif field[yi][xi] ~= nil then
    if xi == 9 then
      if solve(field, 1, yi + 1) then
        return true
      end
    else
      if solve(field, xi + 1, yi) then
        return true
      end
    end
  else
    for i = 1, 9 do
      if check(field, xi, yi, i) then
        field[yi][xi] = i
        if xi == 9 then
          if solve(field, 1, yi + 1) then
            return true
          end
        else
          if solve(field, xi + 1, yi) then
            return true
          end
        end
      end
    end
    field[yi][xi] = nil
    return false
  end
  return false
end

function check(field, xi, yi, i)
  for j = 1, 9 do
    if field[yi][j] == i then
      return false
    end
  end
  for j = 1, 9 do
    if field[j][xi] == i then
      return false
    end
  end
  local xb = ((xi - 1) // 3) * 3 + 1
  local yb = ((yi - 1) // 3) * 3 + 1
  for xii = xb, xb + 2 do
    for yii = yb, yb + 2 do
      if field[yii][xii] == i then
        return false
      end
    end
  end
  return true
end

local b = solve(field)
print_field(field)

Example