**IMPORTANT BUG** Kai'sa improve abilities through purchasing/undo bug
Kai'sa can improve her abilities by buying a certain amount of a stat like AD, AS, or AP. One can purchase an item that has one of those stats and then sell it. This grants the progress towards the improvement for the sample stat and then grants the gold back to be used for improving the another stat through purchasing a different item. I just did it in a bot game. Only had bloodthirster and zeal and was able to improve Q to max and unlock the bonus and still be halfway to E bonus improvement.
Unless this of course is feature...which I wouldn't put past Riot to think it was fair. Either way, not the intended spirit of the champ skill.
EDIT: I want to add that this is exploitable, niche broken, and fits most of Rot's checkboxes for a must-fix bug. As explained by a primer on why Rot doesn't fix many of the bugs it encounters.