I bought a packet of fruit gums and ate $$2$$ of them, secretly, in my Music lesson.  At break, I shared one third of the remaining fruit gums with my friends. I then finished the fruit gums, eating an equal amount in each of the next four lessons.  What is the smallest number of fruit gums there could have been in the packet? 
Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base