Discrete Math Problem 3 (Bonus). The police have three suspects for the murder o
ID: 3047202 • Letter: D
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Discrete Math
Problem 3 (Bonus). The police have three suspects for the murder of Mr. Body: Professor Plum, Ms. Scarlett, and Mr. Green. Plum, Scarlett, and Green each declare that they did not kill Mr. Body. Plum also states that Mr. Body was a friend of Scarlett and that Green disliked him. Scarlett also states that he did not know Mr. Body and that he was out of town the day Mr. Body was killed. Green also states that he saw both Plum and Scarlett with Mr. Body the day of the killing and that either Plum or Scarlett must have killed him. Can you determine who the murderer was if a. one of the three people is guilty, the two innocent people are telling the truth, but the statements of the guilty man may or may not be true? b. innocent people do not lie? Problem 4 (Bonus). South Dakota has fifty senators. Each senator is either honest or corrupt. Suppose you know that at least one of the South Dakotan senators is honest and that, given any two South Dakotan senators, at least one is corrupt. Based on these facts, can you determine how many South Dakotan senators are honest and how many are corrupt? If so, what is the answer?Explanation / Answer
Now, Plum, Scarlett and Green each declare that they did not kill Mr. Body
Plum states that Mr. Body was a friend of Scarlett and Green dislikes him
Scarlett states that he did not know Mr. Body and was out of town the day Mr. Body was killed
Green states that he saw both plum and scarlett with body on the day of the killing
1a. Now if one of the three is guilty, and the two inncocent people are telling the truth and the statements of the guilty may or may not be true then it Mr. Scarlett who must have committed the murder as Plum and scarlett contradict each other, and also Scarlett and Green contradict each other, but Plum and Green are not contradicting each other, in fact both of them are corroborating each other by saying that scarlett was a friend of body and was with him on the day of the murder.
Hence it is Mr. Scarlett who as committed the murder
b. If innocent people did not lie, then too it would be Mr, Scarlett who has committed the murder, as it is only Plum and Green who are not contradictng each other as explained above
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