Find upper bound on number of grandparents











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There is a group of $20$ children and a group of $n$ grandparents to these children. Each of these grandparents is either father's father or mother's father to at least one of these children. Now, following constraints are given:




  1. Each pair of children has at least one grandparent in common who is also present in this group of grandparents.

  2. Every grandparent has at least two grandchildren in this group of children.


Find upper bound on $n$, the number of grandparents present in the group such that above constraints can be satisfied.






combinatorics







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  • I have a solution with $n=11$ grandfathers. What is your largest value so far?
    – Christian Blatter
    Nov 20 at 16:37










  • I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
    – meet112
    Nov 20 at 16:46








  • 1




    Add your solution to the question!
    – Christian Blatter
    Nov 20 at 17:28















up vote
1
down vote

favorite












There is a group of $20$ children and a group of $n$ grandparents to these children. Each of these grandparents is either father's father or mother's father to at least one of these children. Now, following constraints are given:




  1. Each pair of children has at least one grandparent in common who is also present in this group of grandparents.

  2. Every grandparent has at least two grandchildren in this group of children.


Find upper bound on $n$, the number of grandparents present in the group such that above constraints can be satisfied.






combinatorics







share|cite|improve this question
























  • I have a solution with $n=11$ grandfathers. What is your largest value so far?
    – Christian Blatter
    Nov 20 at 16:37










  • I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
    – meet112
    Nov 20 at 16:46








  • 1




    Add your solution to the question!
    – Christian Blatter
    Nov 20 at 17:28













up vote
1
down vote

favorite









up vote
1
down vote

favorite











There is a group of $20$ children and a group of $n$ grandparents to these children. Each of these grandparents is either father's father or mother's father to at least one of these children. Now, following constraints are given:




  1. Each pair of children has at least one grandparent in common who is also present in this group of grandparents.

  2. Every grandparent has at least two grandchildren in this group of children.


Find upper bound on $n$, the number of grandparents present in the group such that above constraints can be satisfied.






combinatorics







share|cite|improve this question















There is a group of $20$ children and a group of $n$ grandparents to these children. Each of these grandparents is either father's father or mother's father to at least one of these children. Now, following constraints are given:




  1. Each pair of children has at least one grandparent in common who is also present in this group of grandparents.

  2. Every grandparent has at least two grandchildren in this group of children.


Find upper bound on $n$, the number of grandparents present in the group such that above constraints can be satisfied.






combinatorics




combinatorics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 20 at 10:34

























asked Nov 20 at 10:29









meet112

416




416












  • I have a solution with $n=11$ grandfathers. What is your largest value so far?
    – Christian Blatter
    Nov 20 at 16:37










  • I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
    – meet112
    Nov 20 at 16:46








  • 1




    Add your solution to the question!
    – Christian Blatter
    Nov 20 at 17:28


















  • I have a solution with $n=11$ grandfathers. What is your largest value so far?
    – Christian Blatter
    Nov 20 at 16:37










  • I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
    – meet112
    Nov 20 at 16:46








  • 1




    Add your solution to the question!
    – Christian Blatter
    Nov 20 at 17:28
















I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 at 16:37




I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 at 16:37












I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 at 16:46






I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 at 16:46






1




1




Add your solution to the question!
– Christian Blatter
Nov 20 at 17:28




Add your solution to the question!
– Christian Blatter
Nov 20 at 17:28















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