Planting Trees 2
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A few weeks after your first job, the mathematics professor calls you back. She was so pleased with your creative solution to the four-tree problem that she has another challenge for you.
This time, she wants you to plant ten trees in five straight lines, with exactly four trees in each line. Can you arrange ten trees to satisfy her requirements?
Hint
Trees can belong to more than one line.
Solution
Answer: Arrange the trees in a pentagram (five-pointed star).
Place five trees at the vertices of a regular pentagon. These form the five outer points of the star.
Now draw the five diagonals connecting non-adjacent vertices. These lines intersect inside the pentagon, creating five intersection points. Place the remaining five trees at these intersection points. Each diagonal line of the pentagram now passes through exactly four trees.
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