Friday, December 28, 2018

geometry - Can you arrange 36 trees so that there are 9 rows of 8 trees?


How could you arrange 36 trees into 9 rows of 8? (Note that a row is a straight line that can go in any direction.)



Answer




Draw nine lines so that no two are parallel and no three meet in the same place, then place a tree at each intersection point. Every pair of lines intersects, so there are $\binom{9}{2}=36$ trees, each row being one of the nine lines.




Illustration:



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