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**Instructions:**

Mohan went to an Island on which there were three tribes of people. People from one of the tribes always spoke the truth. People from the second tribe always lied. People who belonged to the third tribe spoke truth and lie alternately. The Island had only 3 fruits i.e. apple, mango and banana. Mohan found three people X,Y and Z asked them about their favourite fruits.

Their responses were as follows.

X: I like apple. Y likes mango

Y: Z likes mango. X likes banana

Z: I like apple. X likes banana

If it is known that X, Y and Z belonged to different tribes and each one of them liked a different fruit, then answer the following questions.**Question 1: Who likes apple?**

a) X

b) Y

c) Z

d) cannot be determined**Answer:** (B)**Solution:**

Let us assume that Y belongs to the tribe which always speaks the truth.

So we know that Z likes mango and X likes banana, so Y must like apple.

Now letâ€™s see if the statements by the other people validate or contradict our assumption. X says I like apple which is wrong since we know that Y likes apple. His second statement is that Y likes mangoes. This statement is also wrong since Y likes apples. So since both the statements of X are wrong, he must belong to the tribe of liars. Now if our assumption is correct then Z must be the alternator. Zâ€™s first statement is wrong since Y likes apple. Zâ€™s second statement is that X likes banana. This is true. Hence the statements validate our assumption. So Y is the truth teller, Z is the alternator and X is the lier. Also Z likes mango and X likes banana and Y likes apple.**Question 2: Who belongs to the tribe of truth tellers?**

a) X

b) Y

c) Z

d) cannot be determined**Answer:** (B)**Solution:**

Let us assume that Y belongs to the tribe which always speaks the truth.

So we know that Z likes mango and X likes banana, so Y must like apple.

Now letâ€™s see if the statements by the other people validate or contradict our assumption. X says I like apple which is wrong since we know that Y likes apple. His second statement is that Y likes mangoes. This statement is also wrong since Y likes apples. So since both the statements of X are wrong, he must belong to the tribe of liars. Now if our assumption is correct then Z must be the alternator. Zâ€™s first statement is wrong since Y likes apple. Zâ€™s second statement is that X likes banana. This is true. Hence the statements validate our assumption. So Y is the truth teller, Z is the alternator and X is the lier. Also Z likes mango and X likes banana and Y likes apple.**Question 3: Who belongs to the tribe of alternaters?**

a) X

b) Y

c) Z

d) cannot be determined**Answer:** (C)**Solution:**

Let us assume that Y belongs to the tribe which always speaks the truth.

So we know that Z likes mango and X likes banana, so Y must like apple.

Now letâ€™s see if the statements by the other people validate or contradict our assumption. X says I like apple which is wrong since we know that Y likes apple. His second statement is that Y likes mangoes. This statement is also wrong since Y likes apples. So since both the statements of X are wrong, he must belong to the tribe of liars. Now if our assumption is correct then Z must be the alternator. Zâ€™s first statement is wrong since Y likes apple. Zâ€™s second statement is that X likes banana. This is true. Hence the statements validate our assumption. So Y is the truth teller, Z is the alternator and X is the lier. Also Z likes mango and X likes banana and Y likes apple.**Question 4: Ramesh, Suresh and Mahesh are three people who belong to three different tribes of people. The three tribes are known as knights (those who always speak the truth), Knaves(who always lie) and Alters(those who alternatively speak the truth and lie).Ramesh said that Suresh is not an alter. Mahesh said that Ramesh is an alter.Who among the following is Knave?**

a) Suresh

b) Ramesh

c) Mahesh

d) Cannot be determined

In both the cases, Suresh is the Knave. So option A is correct

Since we only have 3 people, we can list down the possible cases. Let T denote the knights, L denote the knaves, and A denotes the alters.

Then possible arrangements are

TLA, TAL, ATL, ALT, LAT, LTA

Ramesh said that Suresh is not an alter, so we can remove the cases TAL and LTA. This is because if Ramesh is a knight then Suresh can not be an alter and if Ramesh is a knave than Suresh is an alter. So we have 4 cases left which are

TLA, ATL, ALT,LAT

Mahesh says that Ramesh is an alter, so using this statement we can rule out cases LAT and ATL.

So we have two cases which are left these are TLA and ALT

From these cases, Ramesh can either be a knight or an alter, Suresh is a knave and Mahesh can also be either knight or an alter.

Ramesh said that Suresh is not an alter. Mahesh said that Ramesh is an alter.

Who is the Knight?

a) Suresh

b) Ramesh

c) Mahesh

d) cannot be determined

So we cannot determine that who is the knight and who is alter. Hence correct option is cannot be determined.

Since we only have 3 people, we can list down the possible cases. Let T denote the knights, L denote the knaves, and A denotes the alters.

Then possible arrangements are

TLA, TAL, ATL, ALT, LAT, LTA

Ramesh said that Suresh is not an alter, so we can remove the cases TAL and LTA. This is because if Ramesh is a knight then Suresh can not be an alter and if Ramesh is a knave than Suresh is an alter. So we have 4 cases left which are

TLA, ATL, ALT,LAT

Mahesh says that Ramesh is an alter, so using this statement we can rule out cases LAT and ATL.

So we have two cases which are left these are TLA and ALT

From these cases, Ramesh can either be a knight or an alter, Suresh is a knave and Mahesh can also be either knight or an alter.

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