Find upper bound on number of grandparents
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:
- 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 at 10:29
meet112
416
add a comment |
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:
- 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 at 10:29
meet112
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
add a comment |
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:
- 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 at 10:29
meet112
416
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 at 10:29
meet112
416
asked Nov 20 at 10:29
meet112
416
edited Nov 20 at 10:34
asked Nov 20 at 10:29
meet112
416
asked Nov 20 at 10:29
meet112
416
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
add a comment |
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
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3006162%2ffind-upper-bound-on-number-of-grandparents%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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