Convex Shapes
Geometry
Level
3
When you place 5 dots at random, you can always find some 4 dots to form a convex quadrilateral. What is the fewest amount of dots needed such that you can always find some 5 dots that will form a convex pentagon?
The answer is 9.
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1 solution
This problem is known as the happy ending problem. It is about finding the minimum amount of dots needed to make a convex polygon. The formula for N<6 is M=1+2^(N-2) where M is the minimum number of dots needed and N is the number of sides in the polygon. 1+2^(5-2)= 1+2^3=1+8=9.
Thus, the answer is 9