Difference between revisions of "2017 AMC 12A Problems/Problem 5"
Thomas0115 (talk | contribs) (→See Also) |
|||
Line 14: | Line 14: | ||
{{AMC10 box|year=2017|ab=A|num-b=7|num-a=9}} | {{AMC10 box|year=2017|ab=A|num-b=7|num-a=9}} | ||
{{AMC12 box|year=2017|ab=A|num-b=4|num-a=6}} | {{AMC12 box|year=2017|ab=A|num-b=4|num-a=6}} | ||
+ | {{MAA Notice}} |
Revision as of 18:16, 8 February 2017
Problem
At a gathering of people, there are people who all know each other and people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur?
Solution
Let the group of people who all know each other be , and let the group of people who know no one be . Handshakes occur between each pair such that and , and between each pair of members in . Thus, the answer is
See Also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2017 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.