Arranging Rose Bushes

Date: 9/13/95 at 15:42:28
From: Christine Heffernan
Subject: Question to be answered

Hi Dr. Math - 

This is the first time I've tried this. Here's a question.

A gardener laying out a rosebed found she could plant 7 rose bushes in 
such a way that they formed 6 straight lines with 3 rose bushes in each 
line. How was this possible?  Show a diagram.

(b) How could she plant 10 rosebushes so that she has 5 lines with 4 
rosebushes in each?

For the questions, the distance between rosebushes does not have to 
be equal.

That's it. Good Luck and thanks in advance.
Gavin

Date: 9/13/95 at 17:20:56
From: Doctor Steve
Subject: Re: Question to be answered

Try laying out the bushes in circular patterns.

Write us back if you want more hints.

-Doctor Steve,  The Geometry Forum

Date: 9/13/95 at 21:30:52
From: Christine Heffernan
Subject: Re: Question to be answered

I've been trying that for a while now and I'm still completely stuck on 
both parts of the question!

I think I need more help!
Thanks

Date: 9/13/95 at 21:42:26
From: Doctor Steve
Subject: Re: Question to be answered

Try putting six bushes in a circle and one in the middle.  Now look for 
your six straight lines with 3 bushes in each.

- Doctor Steve,  The Geometry Forum

Date: 01/17/2001 at 08:39:20
From: Peter Bradford
Subject: Rose Bushes

There is an error in your answer.

Unless you consider a straight line as TWO straight lines, depending on 
which end you start, there are only 3 rows by this method.

The true solution is to put 3 bushes at the corners of an equilateral 
triangle. Three more, each at the midpoint of a side of the triangle. 
Finally, the seventh bush is placed at the centroid of the triangle.

Date: 01/18/2001 at 13:45:49
From: Doctor Greenie
Subject: Re: Rose Bushes

The writer says "the true" solution is with 3 bushes at the corners of 
an equilateral triangle...

The way I read the original problem, it is solved with the first 3 
bushes at ANY points forming a triangle, the next 3 bushes at the 
medians of that triangle, and the 7th bush at the point of intersection 
of those medians.

-Doctor Greenie