Final answer:
The nine-dot problem and the matchstick problems are difficult to solve due to functional fixedness and mental set.
Step-by-step explanation:
The nine-dot problem and the matchstick problems are hard to solve primarily because of functional fixedness and mental set. Functional fixedness is the inability to see an object being used for something other than its intended use, while mental set is the persistence in approaching a problem in a way that has worked in the past but is not working now. Both of these cognitive biases can limit creativity and hinder problem-solving.