IPT2018-Problem8- Candle Lighting Trick (Ecole Polytechnique,France)

IPT2018 Problem 8 Candle Lighting Trick Ecole Polytechnique: It is possible to relight a candle that has just been blown out by lighting the smoke that is created in the process. Indeed, the smoke contains vaporized wax which is the substance that burns in the flame in the first place. What is the maximum distance (between the match and the candle) from which one can relight the candle? Identify the important parameters and find how they influence this maximal distance.