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For small examples, it is a fairly simple process to provide the test-takers with such a choice. For example, if an exam contains 12 questions each worth 10 points, the test-taker need only answer 10 questions to achieve a maximum possible score of 100 points.
The question is whether knowing the warden's answer changes the prisoner's chances of being pardoned. This problem is equivalent to the Monty Hall problem; the prisoner asking the question still has a 1 / 3 chance of being pardoned but his unnamed colleague has a 2 / 3 chance.
Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn). 1-planarity [1] 3-dimensional matching [2] [3]: SP1 Bandwidth problem [3]: GT40 Bipartite dimension [3]: GT18 Capacitated minimum spanning tree [3]: ND5
Solve an equation [14] Also suggested: Look for a pattern [15] Draw a picture [16] Solve a simpler problem [17] Use a model [18] Work backward [19] Use a formula [20] Be creative [21] Applying these rules to devise a plan takes your own skill and judgement. [22] Pólya lays a big emphasis on the teachers' behavior.
Examples of problems that can be modeled as a constraint satisfaction problem include: Type inference [3] [4] Eight queens puzzle; Map coloring problem; Maximum cut problem [5] Sudoku, crosswords, futoshiki, Kakuro (Cross Sums), Numbrix/Hidato and many other logic puzzles; These are often provided with tutorials of CP, ASP, Boolean SAT and SMT ...
These studies have shown that active problem solving early in the learning process is a less effective instructional strategy than studying worked examples (Sweller and Cooper, 1985; Cooper and Sweller, 1987). Certainly active problem solving is useful as learners become more competent, and better able to deal with their working memory limitations.
21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, ... Numbers of the form pq where p and q are distinct primes congruent to 3 (mod 4). A016105: Magic numbers: 2, 8, 20, 28, 50, 82, 126, ... A number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. A018226: Superperfect numbers
The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. [1] Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is ...