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Trees had to be planted in 9 straight rows with each row  having 5 trees. Only had 19...

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justine307 | Student, Undergraduate | eNotes Newbie

Posted January 6, 2010 at 8:49 AM via web

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Trees had to be planted in 9 straight rows with each row  having 5 trees. Only had 19 seeds for trees. How to plant 9 rows with 5 trees?

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amarang9 | College Teacher | (Level 1) Educator Emeritus

Posted January 6, 2010 at 1:52 PM (Answer #1)

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The key for this problem is to intersect as often as you can, and to keep in mind that the seeds do not necessarily have to have the same distance between them.

Draw a 5 pointed star.

 

                                  A

                                 /  X   

B ---------------------------------------------C

      X             /                          X            /

           X       /                             X         / 

               X                                        X                 

            /     X                                 /       X   

        /            X                           /              X

D------------------------------------------------E

                                X    /    

                                  F

                                 

                              

                                             

Then connect A-F, B-E, and D-C. Each edge(point): point of intersection is where a seed should be planted.  It's much easier to draw this on paper and then circle the intersected points. Obviously, you should have 19 points.

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krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted January 6, 2010 at 2:54 PM (Answer #2)

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As suggested in the answer above you can arrange 19 trees in such a way that they form 9 straight lines, each having  5 trees by arranging them in a star formation. But this has to be a star with 6 points rather than 5.

This arrangement is like two equilateral triangles one pointing upward and the other pointing downward superimposed on each other. This arrangement will look some what like the figure below.

In this diagram please consider only the asterisks (*). The hyphens (-) have been drawn just to ensure proper spacing of the asterisks.

 

------------------*A

 

*F          *      *      *          *E

---------*                    *

-----*              *             *

---------*                    *

*B          *      *      *          *C

 

-----------------*D

In the above figure vertices of the two triangles are represented by ABC and DEF. Please note that in this arrangement each line of the two triangles has 5 points or trees. additional three rows of trees with five trees in each is formed by joining opposite vertices of two triangles - that is, AD, BE and CF.

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