Importance of Problem-Solving and the Trial-and-Error Strategy

Supporting and Learning Mathematics
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Professor's Name Date Understanding the importance of problem-solving is essential for any individual. This set of skills is essential for various aspects of life, whether in school, career, or in day-to-day usage, for it trains the student's mind to think critically based on the specific set of circumstances, rather than simply memorize them (Wismath, et al., 2014). In other words, problem-solving allows us to reconfigure our previous memories and skillset to solve a pre-existing problem. Accordingly, this article would focus on the problem-solving skills involved in solving a 3x3 grid in which the differences between each joined square should be odd (Figure 1). Based on the author's experience, he believes that solving a problem would be much easier for everyone by using trial and error techniques and a systematic approach. Figure 1 - 3x3 Squares Problem Solving Problem Solving Strategy             Answering problems could include various strategies to reach the pre-determined goal, one of which is trial-and-error. According to Cherry (2020), Trial-and-Error is one of the most commonly used problem-solving strategies that "involves trying a number of different solutions and ruling out those that do not work." However, despite the effectiveness of this strategy, it must be noted that trial-and-error is one of the most time and effort-consuming strategies, especially when it is done randomly. This is because of the many possible strategies and approaches, which might present their flaws later in the problem-solving step (Schneider, n.d.). Therefore, trial-and-error is most effective when there is a limited number of options.             Going back to the 3x3 Grid, it is clear that there are a lot of possible configurations even though only a few would fit the activity's objective. For example, since the middle tile (E) has four (4) connections with other tiles (B, D, F, and H), this means that the number inside should be the right one so that the difference between the adjacent and the middle tiles would equal to an odd number. Additionally, even after we figure the number of the middle tile and the four adjacent ones, such configuration should also fit the remaining tiles (A, C, G, and I) so that the remaining numbers would also result in an odd difference. In other words, this shows the sheer number of configurations that are possible, thereby showing that a trial-and-error method would result in a vast number of possible combinations.             In order to reduce the number of combinations, I initially focused on determining the "difference" that each adjacent tile should have. Since the instructions said that the numbers to be placed within the Grid would only be from 1 to 9, this means that the largest possible difference between them is 8 (9-1=8). However, given that the resulting difference should only be odd, then we should consider seven (7) instead of eight (8). After getting this, we then extract the other possible odd differences to limit our choices, resulting in n = "1,...