Maths Olympiad Prep

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Problem 348

Combinatorics Difficulty 2.5 Find the answer Junior Mathematical Olympiad · Netherlands

Dotty has drawn a paper with six dots on it, no three of which lie on a line. With a pen, she draws a straight line from a certain dot to another dot. Then, without lifting her pen, she draws a straight line to a dot she has not visited before. She continues like this until she has visited all the dots. Finally, she draws a straight line from the last dot to the first dot.
How many figures can Dotty make this way?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

60

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.