2006 Seniors Pancyprian/2nd grade/Problem 5

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 that nobody is sitting between two girls. If there are two girls, there are two boys in between them to minimize the number of boys (). We can see that there are twice as many boys are girls, contrary to the problem condition. Therefore, someone must be sitting between two girls.

~MathFun1000 (Readability)

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See also

• Seniors Pancyprian Competition
• Seniors Pancyprian Problems and Solutions
• Mathematics competition resources