Suppose You Have 5 Coins, One of Which Is Counterfeit

question 3

Essay

Suppose you have 5 coins, one of which is counterfeit (either heavier or lighter than the other four). You use a pan balance scale to find the bad coin and determine whether it is heavier or lighter.
(a) Prove that 2 weighings are not enough to guarantee that you find the bad coin and determine whether it is heavier or lighter.
(b) Draw a decision tree for weighing the coins to determine the bad coin (and whether it is heavier or lighter) in the minimum number of weighings.

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Definitions:

Lewin

Lewin, often referred to as Kurt Lewin, was a pioneering psychologist known for his contributions to social, organizational, and applied psychology.

Stages

Distinct phases or periods within a process or event, characterized by particular features or activities.

Resistance to Change

The reluctance or refusal to adapt to new methods, practices, or conditions within an organization or personal life.

Organizations

Groups or collectives of people structured and managed to meet a need or pursue collective goals on a continuing basis.