As of now, there are no known algorithms that are proven to be unsolvable, but there are many problems for which no efficient algorithm is known. In fact, one of the most famous open problems in computer science is whether or not there exists an algorithm that can solve the Traveling Salesman Problem (TSP) in polynomial time, which means that the running time of the algorithm would be proportional to a polynomial function of the size of the input.

The TSP is an optimization problem that involves finding the shortest possible route that visits a given set of cities and returns to the starting point. While there are algorithms that can solve the TSP, they are generally very slow and are not guaranteed to find the optimal solution for larger problem sizes.

Other examples of problems for which no efficient algorithm is known include the knapsack problem, the graph coloring problem, and the maximum clique problem. These are all NP-hard problems, which means that any solution to them can be verified in polynomial time, but finding a solution may require exponential time.

While it is theoretically possible that there may be problems that are unsolvable by any algorithm, it is not currently known whether such problems exist. However, the concept of unsolvable problems is an important one in computer science and mathematics, and the study of these problems has led to many important insights into the nature of computation and complexity.
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