# HypothetiCo: Scale Challenge Logic Problem

In this situation, it is required to identify an item that differs from the rest of the beams for a limited number of scales using. The search for a solution in this case is carried out by comparing operations, however, not only single elements, but also groups of elements with each other (Ding et al., 2020). Problems of this type are most often solved by logical reasoning.

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The fastest way to weigh beams is to divide them into three equal groups, and then weight them by turns. Twenty-seven beams represent three groups of nine beams, it is necessary to weigh them. Since the scales are very large and can hold even all twenty-six beams at once, the task condition allows to do this. The first step will be a comparison on two scales of two groups of nine beams each. The third group of nine beams does not need to be used yet, we put it aside. Next, the HypothetiCo company should work with the outweighed beams group, remove the rest. If the scales show equality, then the defective beam is in the third pile, which was previously postponed. In this case, it is necessary to continue working with it. In total, after the first weighing, there is a beams group consisting of nine pieces, one of which is guaranteed to be defective.

A group of nine beams can also be divided into three equal groups of three beams. During the second weighing, two groups of three beams should be placed on the scales, putting one aside. Next, the company should again work with the outweighed beams group. If the scales show equality, then the defective beam is in the third group, which was postponed earlier. In this case, it is necessary to work with it. In total, after the second weighing, there is a group of beams consisting of three pieces, one of which is guaranteed to be defective. Or, if there was equality on the scales, the defective one is in three deferred beams. The third weighing will show a defective beam. Since there is a group of three beams left, the company can weigh any two. The outweighed beam will be defective; if there is equality on the scales, then the third beam is guaranteed to be defective.

It can definitely be said that the logical task is connected with the science of reasoning. Therefore, this task contains a non-standard element that distinguishes it from most tasks on this topic. At the same time, non-standardless is manifested both in the condition itself (working with a supplier) and in the solution methods (weighing by groups). Artificial techniques were not used in solving the logical problem. The decision was based on reasoning that led to an interesting answer.

Weighing tasks are a type of math problems in which it is required to establish a particular fact by weighing on lever scales without a dial. Beams were used as weighed objects in this case. The formulation of the problem required to determine the minimum number of weighing required to identify a defective beam. This need was due to the difficulty of working with scales due to their bulkiness and the large weight of beams. During the search for a solution, empirical methods were used. The provided solution showed an algorithm for determining this fact in the least number of weighing.

## Reference

Ding, R. X., Palomares, I., Wang, X., Yang, G. R., Liu, B., Dong, Y., … Herrera, F. (2020). Large-scale decision-making: Characterization, taxonomy, challenges and future directions from an Artificial Intelligence and applications perspective. Information Fusion, 59(7), 84-102.

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