The puzzle has two ways to solve it. I prefer putting the fire out - it's more satisfying. The advice in the guide assumes that you've kept your fire going. If you've let it burn out for more that a few hours at a time, it will take longer. There is nothing wrong with that puzzle in your game (although the latest version is 1.00.04 - see Arthur's post), you just need to be patient and keep a nice fire burning.