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The problem format and the structural type of analog presentation showed the highest positive transference to problem solving. The researcher suggested that a well-thought and planned analogy relevant in format and type to the problem-solving task to be completed can be helpful for students to overcome functional fixedness.
Closer to the Collatz problem is the following universally quantified problem: Given g, does the sequence of iterates g k (n) reach 1, for all n > 0? Modifying the condition in this way can make a problem either harder or easier to solve (intuitively, it is harder to justify a positive answer but might be easier to justify a negative one).
The problem of induction is a philosophical problem that questions the rationality of predictions about unobserved things based on previous observations. These inferences from the observed to the unobserved are known as "inductive inferences". David Hume, who first formulated the problem in 1739, [ 1] argued that there is no non-circular way to ...
Eureka effect. The eureka effect (also known as the Aha! moment or eureka moment) refers to the common human experience of suddenly understanding a previously incomprehensible problem or concept. Some research describes the Aha! effect (also known as insight or epiphany) as a memory advantage, [ 1][ 2] but conflicting results exist as to where ...
The following is a list of notable unsolved problems grouped into broad areas of physics. [ 1] Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in ...
The word heuristic is taken directly from the Greek verb, heuriskein, 'to discover'. As a noun it is defined as 'a technique of discovery' and as an adjective, it means 'serving to guide, discover, or reveal'. The more common designation for all of this is 'the discovery method'.
Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer. For other problems, such as the 5th, experts have ...
The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved. Here, quickly means an algorithm that solves the task and runs in polynomial time exists, meaning the task completion time varies as a polynomial ...