Research on problem solving has mostly examined solvable tasks. However, in real life, we encounter more often problems that have no apparent solutions. Given the lack of research on problem solving when faced with unsolvable problems, we investigated the effect of giving information about the presence of unsolvable anagrams among solvable ones. In Experiment 1, for the same set of anagrams, half of the college students were informed about the presence of unsolvable anagrams and the other half were not. Some of the anagrams were either very difficult or unsolvable. The results showed that the uninformed group outperformed the informed one and the former group spent more time on the task. We replicated the results in Experiment 2 in a within-subject design. However, when there were no difficult or unsolvable items, in Experiment 3, there was no difference between the two groups. These findings suggest that the information about solvability of a problem strongly influences the effort spent and thus the accuracy on the task only when there were difficult or unsolvable items.