WIPRO PUZZLES Recent Paper

A, B, C and D are related to each other.

* One of the four is the opposite sex from each of the other three.

* D is A's brother or only daughter.

* A or B is C's only son.

* B or C is D's sister.

How are they related to each other?

Answer

A, B & D are males; C is female. B is C's only son. A & D are C's brothers.

A(male) --- C(female) --- D(male)

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B(male)

Work out which relation can hold and discard the contradictory options.

From (2) and (4), D can not be a only daughter and have a sister (B or C). Hence, D is A's brother i.e. D is a Male.

From (4), let's say that B is D's sister i.e. B is Female.

From (3), A is C's only son i.e. A is Male.

But D is A's brother which means that A is not C's only son. Hence, our assumption was wrong.

Thus, C is D's sister i.e. C is Female. And B must be C's only son.

Now it is clear that D & B are Males and C is Female. A must be a Male as only one of them is of opposite sex from each of the other three. And he is C & D's brother.

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Brain Teaser No : 00404

At the party there were 19 females, 12 males, 14 adults and 17 children. Then I arrived and the number of different man-woman couples possible became equal to the number of boy-girl couples possible.

Who am I - a man, a woman, a boy or a girl?

Note that if there were 9 boys and 8 girls at the party, then there would have been 72 (9x8) boy-girl couples possible.

Answer

I am a Girl and there were 9 men, 5 women, 3 boys and 14 girls before I arrived at the party.

Before I arrived, let M be the number of male adults (men) at the party.

Then, the number of female adults (women) = 14 - M

The number of boys = 12 - M

The number of girls = 5 + M

Now, I arrived at the party and I am either a man or a woman or a boy or a girl. Let's consider each case one-by-one.

Case I: Let's assume that I am a Man. It is given that after I arrived, the number of different man-woman couples possible became equal to the number of boy-girl couples possible. Hence,

(M + 1) * (14 - M) = (12 - M) * (5 + M)

14M - M2 + 14 - M = 60 + 12M - 5M - M2

13M + 14 = 60 + 7M

6M = 46

This is impossible as the value of M must be integer.

Case II: Let's assume that I am a woman, then the equation is

(M) * (15 - M) = (12 - M) * (5 + M)

15M - M2 = 60 + 12M - 5M - M2

15M = 60 + 7M

8M = 60

This is also impossible as the value of M must be integer.

Case III: Let's assume that I am a boy, then the equation is

(M) * (14 - M) = (13 - M) * (5 + M)

14M - M2 = 65 + 13M - 5M - M2

14M = 65 + 6M

8M = 65

This is also impossible as the value of M must be integer.

 

Case IV: Let's assume that I am a girl, then the equation is

(M) * (14 - M) = (12 - M) * (6 + M)

14M - M2 = 72 + 12M - 6M - M2

14M = 72 + 6M

8M = 72

M = 9

Thus, I am a Girl and there were 9 men, 5 women, 3 boys and 14 girls before I arrived at the party.

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Brain Teaser No : 00038

The population of an island consists of two and only two types of people : the knights, who invariably tell the truth and the knaves who always lie.

* three of the inhabitants called X, Y and Z were standing together. A newcomer to the island asked, "Are you a knight or a knave?" X mumbled his answer rather indistinctly, so the stranger could not quite make out what he had said. The stranger than asked Y, "What did X say?" Y replied, "X said that he was a knave." Whereupon Z said, "Don't believe Y, he's lying." What are Y and Z?

* Suppose that the stranger asked X, instead, "How many knights among you?" Again X replies indistinctly. So the stranger asks Y, "What did X say?" Y replies, "X said that there is one knight among us." Then Z says, "Don't believe Y, he is lying!" Now what are Y and Z?

* There are only two inhabitants, X and Y. X says, "At least one of us is a knave." What are X and Y?

* Suppose X says, "Either I am a knave, or Y is a knight?" What are X and Y?

* Consider once more X, Y and Z each of who is either a knight or a knave. X says, "All of us are knaves." Y says, "Exactly one of us is a knight." What are X, Y and Z?

Answer

Teaser 1 : A Simple one. The statement made by Y is false - "X said that he was a knave".

Case 1 Case 2 Case 3 Case 4

X Knight Knight Knave Knave

Y Knight Knave Knight Knave

Analyse the above 4 cases. In all the cases statement made by Y is contradicory and therefore false. Hence, Y is Knave and Z is Knight.

Teaser 2 : Again the statement made by Y is false - "X said that there is one knight among us". Analyse these statement with 4 possible cases as above. In all the cases statement made by Y is false. Hence, Y is Knave and Z is Knight.

Teaser 3 : X is Knight and Y is Knave.

Teaser 4 : Both are Knight.

Teaser 5 : X and Z are Knaves, Y is Knight.