In$$ Paul's bicycle$$ shop, $40$ bikes are inspected. If $20$ needed new tires and $29$ needed gear$$ repairs, answer the following questions.

$$a$)$ What is the greatest number of bikes that could have needed$$ both?

$$b$)$ What is the least number of bikes that could have needed$$ both?

$$c$)$ What is the greatest number of bikes than could have needed$$ neither?