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Question

There are three fathers and six sons in a room. If every father's son(s) and every son's father are present, then the minimum number of individuals in the room are

The correct answer is
7

Minimum Individuals in Room Riddle Solution

The question asks for the minimum number of people required in a room that contains exactly 3 fathers and 6 sons. An important condition is that "every father's son(s) and every son's father are present," implying a complete set of relationships within the group. To find the minimum number, we must maximize the overlap in roles, where one person can be both a father and a son.

Minimum Structure for 7 Individuals

The minimum number of individuals required is 7. This can be achieved with a structure spanning three generations:

  • Individual 1: The Grandfather. (Serves as Father 1)
  • Individual 2: Son 1 (son of Individual 1). (Serves as Son 1 and Father 2)
  • Individual 3: Son 2 (son of Individual 1). (Serves as Son 2 and Father 3)
  • Individual 4: Grandson 1 (son of Individual 2). (Serves as Son 3)
  • Individual 5: Grandson 2 (son of Individual 2). (Serves as Son 4)
  • Individual 6: Grandson 3 (son of Individual 3). (Serves as Son 5)
  • Individual 7: Grandson 4 (son of Individual 3). (Serves as Son 6)

Verification of Conditions

Let's verify if this group of 7 people meets all the conditions:

  • Total People: There are exactly 7 individuals.
  • Fathers:
    • Individual 1 (Grandfather) is a father.
    • Individual 2 (Son 1) is a father.
    • Individual 3 (Son 2) is a father.
    This gives a total of 3 fathers.
  • Sons:
    • Individual 2 is a son (of Individual 1).
    • Individual 3 is a son (of Individual 1).
    • Individual 4 is a son (of Individual 2).
    • Individual 5 is a son (of Individual 2).
    • Individual 6 is a son (of Individual 3).
    • Individual 7 is a son (of Individual 3).
    This gives a total of 6 sons.

All conditions are satisfied with 7 individuals, confirming this as the minimum number required.

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Important Questions from Blood Relations (Notes)

  1. Introducing a man, a women said, "His wife is the only daughter of my father". How is that man related to the woman?
  2. There are six members A, B, C, D, E and F in a family. E is daughter of B and A is brother of B. C is father of A and D is brother of E. F is wife of C. Uncle of D is
  3. In a family, Bhanu is the father of Kamlesh. Bhanu has only two children. Kamlesh is the brother of Ritu. Ritu is the daughter of Santosh. Aryan is the grandson of Santosh. Sunny is the father of Aryan. How is Sunny related to Bhanu ?
  4. In a certain code language, 
    'A + B' means 'A is the son of B', 
    'A - B' means 'A is the sister of B', 
    'A x B' means 'A is the wife of B' and 
    'A ÷ B' means 'A is the father of B. 
    How is Q related to D if ‘Q + E ÷ R – C x D'?

  5. H is the brother of A. R is the sister of K. P is the son of K. K is the wife of A. How is H related to R?
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