Clara had never had to fend for herself. As such, she had always been able to devote her time to learning things which were infinitely more interesting to her, but of no use in this situation.
Off the top of her head, Clara could think of several spells which would easily start a fire in the fireplace. Hell, she could think of several spells which would start fires all over the common room, occupants included. None of those spells, though, were of any help considering her wand was behaving like nothing more than a non-magical piece of wood.
"Oh." She bit her lip and thought. The sticks were awfully small, so it made sense that something might be missing. "Have you tried using more than one? Maybe they don't have enough..." Clara paused, not sure what the sticks actually had that was supposed to make fire. "Maybe one isn't strong enough?"