Final answer:
Unsolvable algorithmic problems can occur when there are infinite cases to consider, as no algorithm can handle an infinite set of inputs in a finite amount of time. The halting problem is a well-known example of such an unsolvable problem in the field of theoretical computer science.
Step-by-step explanation:
The unsolvability of an algorithmic problem, particularly when considering an infinite number of cases, may occur under certain circumstances. Option D in your question is correct: Unsolvable problems may arise when dealing with infinitely many cases. This can happen in situations where a problem is defined in such a way that no finite algorithm can solve all possible instances of the problem. A classic example of an unsolvable problem is the halting problem, which determines whether a given computer program will finish running or continue to run indefinitely. Since a program may have an infinite number of inputs, an algorithm that can handle all possible inputs in a finite amount of time does not exist.
Algorithms
While problem solving strategies and algorithms are extensively used both in academics and everyday life, there are limits to what can be algorithmically solved. Theoretical computer science often deals with such limits, exploring questions about computation and its feasibility or infeasibility. In practice, as you become more experienced with problem-solving, you'll find that creativity and insight play crucial roles alongside systematic approaches.