Difference between revisions of "2022 USAMO Problems/Problem 6"
(Created page with "==Problem== There are <math>2022</math> users on a social network called Mathbook, and some of them are Mathbook-friends. (On Mathbook, friendship is always mutual and permane...") |
(→Problem) |
||
| Line 3: | Line 3: | ||
Starting now, Mathbook will only allow a new friendship to be formed between two users if they have at least two friends in common. What is the minimum number of friendships that must already exist so that every user could eventually become friends with every other user? | Starting now, Mathbook will only allow a new friendship to be formed between two users if they have at least two friends in common. What is the minimum number of friendships that must already exist so that every user could eventually become friends with every other user? | ||
| + | |||
| + | |||
| + | ==See also== | ||
| + | {{USAMO newbox|year=2022|num-b=5|num-a=6}} | ||
| + | {{MAA Notice}} | ||
Revision as of 14:43, 27 March 2022
Problem
There are 
users on a social network called Mathbook, and some of them are Mathbook-friends. (On Mathbook, friendship is always mutual and permanent.)
Starting now, Mathbook will only allow a new friendship to be formed between two users if they have at least two friends in common. What is the minimum number of friendships that must already exist so that every user could eventually become friends with every other user?
See also
| 2022 USAMO (Problems • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
