Difference between revisions of "2006 Seniors Pancyprian/2nd grade/Problem 5"
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== Problem == | == Problem == | ||
| − | Fifty persons, twenty five boys and twenty five girls are sitting around a table. Prove that there is a person | + | Fifty persons, twenty five boys and twenty five girls are sitting around a table. Prove that there is a person out of 50, who is sitting between two girls. |
== Solution == | == Solution == | ||
Revision as of 11:21, 10 October 2007
Problem
Fifty persons, twenty five boys and twenty five girls are sitting around a table. Prove that there is a person out of 50, who is sitting between two girls.
Solution
Let's assume the contrary. If there are two girls, there are two boys in between them to minimize the number of boys. But that means that there are twice as many boys as girls, but that's impossible. Therefore, etc.
