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) | | 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. ============================= 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. ========================================= 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.
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