What might cause a cooked sugar solution to crystallize?

Cooking a sugar solution too slowly can lead to crystallization primarily because it allows for the gradual evaporation of water and the concentration of sugar to increase without reaching the appropriate temperature or achieving the right syrup texture. When cooked slowly, the sugar molecules have more time to align and form crystals, as the solution may not be hot enough to fully dissolve the sugar or to reach the desired state, which would maintain the solution in a more amorphous state.

By cooking at a higher temperature, the sugar solubility increases, and rapid cooking helps to prevent sugar crystallization by creating a more saturated syrup. This prevents the formation of sugar crystals, allowing the solution to remain smooth. In contrast, the option focusing on only using pure sugar, or dealing with high humidity conditions, could involve factors that do not directly and consistently induce crystallization in the same manner. Crystallization often occurs as a result of factors such as temperature control and cooking speed rather than solely the purity of the sugar or moisture in the air.