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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. Pointing to a photograph Lata says, "He is the son of the only son of my grandfather."
    How is the man in the photograph related to Lata ?
  2. Introducing a man, a women said, "His wife is the only daughter of my father". How is that man related to the woman?
  3. In a family, D is the father of F and E only. D has one son. E is married to G. G is the son-in-law of P. G has one son H. K and J are the children of E. L is married to K. The total number of male members in the family is :
  4. 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
  5. In a certain code language,
    A + B means ‘A is the mother of B’
    A - B means ‘A is the wife of B’
    A × B means ‘A is the sister of B’
    A ÷ B means ‘A is the father of B’

    Based on the above, how is S related to P if ‘S - K ÷ T × V + P’?
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