They love equilateral triangles and want to create nn equilateral triangles on the grid by adding some straight lines. The triangles must all be empty from the inside (in other words, no straight line or hexagon edge should pass through any of the triangles).
You are allowed to add straight lines parallel to the edges of the hexagons. Given nn, what is the minimum number of lines you need to add to create at least nn equilateral triangles as described?
Adding two red lines results in two new yellow equilateral triangles.
In the first and second test cases only 2 lines are needed. After adding the first line, no equilateral triangles will be created no matter where it is added. But after adding the second line, two more triangles will be created at once.
In the third test case, the minimum needed is 3 lines as shown below.
