Mixing
Find upper bound on number of grandparents
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:
- Each pair of children has at least one grandparent in common who is also present in this group of grandparents.
- 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
asked Nov 20 '18 at 10:29
meet112
516
add a comment |
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:
- Each pair of children has at least one grandparent in common who is also present in this group of grandparents.
- 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
asked Nov 20 '18 at 10:29
meet112
516
I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 '18 at 16:37
I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 '18 at 16:46
1
Add your solution to the question!
– Christian Blatter
Nov 20 '18 at 17:28
add a comment |
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:
- Each pair of children has at least one grandparent in common who is also present in this group of grandparents.
- 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
asked Nov 20 '18 at 10:29
meet112
516
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:
- Each pair of children has at least one grandparent in common who is also present in this group of grandparents.
- 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
asked Nov 20 '18 at 10:29
meet112
516
asked Nov 20 '18 at 10:29
meet112
516
edited Nov 20 '18 at 10:34
asked Nov 20 '18 at 10:29
meet112
516
asked Nov 20 '18 at 10:29
meet112
516
asked Nov 20 '18 at 10:29
meet112
516
516
I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 '18 at 16:37
I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 '18 at 16:46
1
Add your solution to the question!
– Christian Blatter
Nov 20 '18 at 17:28
add a comment |
I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 '18 at 16:37
I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 '18 at 16:46
1
Add your solution to the question!
– Christian Blatter
Nov 20 '18 at 17:28
I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 '18 at 16:37
I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 '18 at 16:37
I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 '18 at 16:46
I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 '18 at 16:46
1
1
Add your solution to the question!
– Christian Blatter
Nov 20 '18 at 17:28
Add your solution to the question!
– Christian Blatter
Nov 20 '18 at 17:28
add a comment |
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I have a solution with $n=11$ grandfathers. What is your largest value so far?
– Christian Blatter
Nov 20 '18 at 16:37
I could do it with $n$=14. Can you please explain how did you arrive at $n$=11?
– meet112
Nov 20 '18 at 16:46
1
Add your solution to the question!
– Christian Blatter
Nov 20 '18 at 17:28