A set of eight points in general position with no convex pentagon. According to a generalization of the <a href="https://en.wikipedia.org/wiki/Happy_Ending_problem" class="extiw" title="en:Happy Ending problem">Happy Ending problem</a>, every nine points in general position have some five points forming a convex pentagon; this example shows that the number of points in this result cannot be reduced.
<a href="https://en.wikipedia.org/wiki/User:David_Eppstein" class="extiw" title="wikipedia:User:David Eppstein">David Eppstein</a> at <a href="https://en.wikipedia.org/wiki/" class="extiw" title="wikipedia:">English Wikipedia</a>
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