A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
How to prove that in group of 6 people there are at least 2 people who has same amount of friends among that group?
 2 years ago
How to prove that in group of 6 people there are at least 2 people who has same amount of friends among that group?

This Question is Closed

rld613
 2 years ago
Best ResponseYou've already chosen the best response.0R u sure it cld be proved

rld613
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see didnt read the question correctly

Tomas.A
 2 years ago
Best ResponseYou've already chosen the best response.2it's classical problem and i have proved it somehow but i don't remember anymore

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0do the 6 people even have to be friends? after all, a group of 6 strangers is still a group of 6

Tomas.A
 2 years ago
Best ResponseYou've already chosen the best response.2no, but if they don't have any friends there will be 6 people who have no friends

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0if 2 people in the group are friends; then at least 2 people have 1 friend .... something like that

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0if 3 people are friends, then a > bc, b > ac, c>ba

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0thats at least 2 with the same amount of friends

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0or even a>c , c>b, c>ab

Tomas.A
 2 years ago
Best ResponseYou've already chosen the best response.2well i translated it from lithuanian but it seems it has same meaning

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0can 2 people be not friends? if one of them is a friend?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2oh wait, I see. Let f(n) be the number of friends in that group that the nth person has. For each n, \[ 0 \leq f(n) \leq 5 \] Therefore ...

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0a>c, b>c , c>ab is what i meant lol

Tomas.A
 2 years ago
Best ResponseYou've already chosen the best response.2yes there can be no friends at all or 1 person can have no friends

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0I think James has it :)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0even if 4 are friends, that still leaves 2 with 0 friends each which is the same amount

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2there are 6 values for f(1), f(2), f(3), f(4), f(5), f(6). Now it can't be that these six number take on all of 0,1,2,3,4,5. Because if f(n) = 5 for one n, then f(j) > 0 for all other \( j \neq n \). Hence in fact, there are only 5 possible values for f(n). But as there are six f(n), at least two of the f(n) must be equal.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0ill concede to that answer as well ;)

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0my by case proof could get lengthy

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0gotta hang it on the left to be a valid q lol

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.0and I gotta get my ode hw written up so ciao yall :)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.