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.

---

Definitions:

Egg Donation

The process by which a woman donates one or several of her eggs (oocytes) for purposes of assisted reproduction or biomedical research.

Informed Consent

The process of obtaining permission from a person before conducting a healthcare intervention, based on a full understanding of the risks, benefits, and alternatives.

Financial Inducements

Payments or incentives typically offered to encourage or persuade individuals or organizations to take a particular action.

Surrogacy Contracts

Legal arrangements where a surrogate agrees to carry and deliver a child for another person or couple, specifying rights, obligations, and expectations of all parties involved.