Question

In: Advanced Math

Puzzle #1 A kindergarten teacher knows that exactly one of four students, Kathy, Andy, Jose, or...

Puzzle #1 A kindergarten teacher knows that exactly one of four students, Kathy, Andy, Jose, or Dana, took Amy’s cookie. When asked about who did it, Kathy said: “Andy did it.”, Andy said: “Dana did it.”, Jose said: “I didn’t do it.”, and Dana said: “Andy lied when he said I did it.” 1. If the teacher knows that exactly one of the students is telling the truth, who did it? Explain.

2. If the teacher knows that exactly one of the students is lying, who did it? Explain. Puzzle #2 There are three neighbors living in a row. Each house has a different color and a different animal and person living in/at the house. Each person has a different profession. The horse lives in the first house. The doctor is Jamal’s neighbor. Jamal does not have a ferret as a neighbor. Carlos does not live in the blue house and Jamal does not live in the green house. Ann is a lawyer and lives in the 3rd house. The professor has the horse as a neighbor. The mouse does not live in the red house. The lawyer does not live in the blue house. 1. Determine the color of the house the horse lives in. This project will be scored out of 10 points in the following way:

Expert Solution

#Puzzle -1
Given: a. Kathy (K) says "Andy did it"
b. Andy(A) says "Dina did it"
c. Jose says "I didn't do it"
d. Dana says "Andy lied when he said that I did it"

Ans 1) To find: Who stole the cookie when exactly one of the students is saying the Truth, i.e., rest are lying.
Here we consider 4 cases:

Case 1: Kathy is telling the Truth ---> i.e the rest 3 (i.e., Andy, Jose and Dana) are lying

Kathy spoke the truth, that means Andy stole the cookies.
Andy lied, that means Dana didn't do it
Jose lied, that means He did it.
Dana lied, that means she did it.
(Here we can see that bullet no.1 and 3 and bullet no.s 2 and 4 are contradicting each other as there is only 1 thief.)
Hence this case can not be considered.

Case 2: Andy is telling the truth,

that means Dana did it.
Also, Kathy lied => Andy didn't do it
Jose lied => He did it
Dana lied => She did it.
All these statements are contradicting each other. Hence case-2 can not be considered.

Case 3: Jose is telling the truth,

which means Jose did it
Kathy lied => Andy didn't do it
Andy lied => Dana didn't do it
Dana lied => Andy didn't lie (contradiction)
Bullet no. 3 and 4 are contradicting each other. Hence case-3 can not be considered

Case 4: Dana is telling the truth, all others (Kathy, Andy, Jose are lying)

Dana spoke the Truth => Andy lied => Dana didn't do it
Kathy lied => Andy didn't do it.
Andy lied => Dana didn't do it
Jose lied => He did it.
All the conditions are satisfied in this case.
Thus Jose is the one who stole the cookies.

Ans. 2) To find: Who stole the cookies when exactly one of the students is Lying i.e., rest are saying the Truth.
Here we consider 4 cases:

Case 1: Kathy lying and Andy, Dana and Jose are truthful.

Kathy lying => Andy didn't do it.
Andy is truthful => Dana did it
Jose is truthful => He didn't do it
Dana is truthful => Andy is lying
(Bullet no. 2 and 4 are contradicting each other. Hence case-1 can not be considered)

Case 2: Andy is lying and Kathy, Jose and Dana are truthful.

Andy lying => Dana didn't do it
Kathy truthful => Andy stole it
Jose truthful => He didn't do it
Dana truthful => Andy lied => Dana didn't do it.
All the conditions are satisfied in this case.
Thus Andy is the one who stole the cookies.

Case 3: Jose is lying,

Jose lied => He did it
Kathy is truthful => Andy did it
Andy is truthful => Dana did it
Dana is truthful => Andy lied
All these statements are contradicting each other. Hence case-3 can not be considered.

Case 4: Dana is lying

Dana lied => Andy spoke truth => Dana stole the cookies
Kathy was truthful => Andy stole it
Jose was truthful => He didn't do it.
Andy was truthful => Dana did it.
Bullet no. 1 and 2 are contradicting each other as there is only 1 thief. Hence this case can not be considered.

#Puzzle -2:
According to the give conditions, the following table can be formed:

	House 1	House 2	House 3
Color	Red	Blue	Green
Animal	Horses	Ferret	Mouse
Person	Carlos	Jamal	Ann
Profession	Doctor	Professor	Lawyer

Thus, the horse lives in a Red colored house.

Colby Messinger answered 2 years ago

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