Planting Trees

Date: 08/13/2002 at 20:09:51
From: D Mann
Subject: Math Puzzle

I have 10 trees to plant. They need to be planted in 5 rows with 4 
trees in each row.  Please help me determine how to plant my trees.

This was a problem in my son's 7th grade math class.

Thank you!

Date: 08/13/2002 at 23:29:12
From: Doctor Peterson
Subject: Re: Math Puzzle

Hi!

This sort of problem is not really a math problem, but a puzzle to 
get the students thinking rather than just following rules. On the 
other hand, there are some ways math can guide your thinking.

Suppose you just had 5 rows of trees, with 4 in each. You would have 
20 trees, which is just twice as many as you want. So it sounds as if 
each tree should be in two rows.

That seems normal; if you had a rectangle of trees, each tree would 
be in one row across and one row (column) down. The trouble is, 
unless you have a square, those rows won't all have the same length, 
and 10 is not a square number. Also, if we think about one of these 
rows, each of the four trees in it has to be in another row, so all 
of the other four rows have to cross this row. None of the rows can 
be parallel.

So you have to be creative. One way to be creative is to look at a 
problem inside out. Rather than draw some trees and try to line them 
up, imagine having five sticks to represent the rows. You have to 
arrange those sticks so that each crosses each of the four other 
sticks; then you can put a tree at each crossing and it will solve 
the problem.

If you have any further questions, feel free to write back.

For more help, see the Math Forum's Rosebush Puzzle:

   http://mathforum.org/k12/k12puzzles/rosebush.puzzle2.html

- Doctors Peterson and Sarah, The Math Forum
  http://mathforum.org/dr.math/