It seemed to the author that it might be worth while to collect and to group questions and suggestionswhich are typically helpful in discussing problems with students. The list we study contains questions andsuggestions of this sort, carefully chosen and arranged; they are equally useful to the problem-solver whoworks by himself. If the reader is sufficiently acquainted with the list and can see, behind the suggestion,the action suggested, he may realize that the list enumerates, indirectly, mental operations typicallyuseful for the solution of problems. These operations are listed in the order in which they are most likelyto occur.