Associated Topics || Dr. Math Home || Search Dr. Math

### 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

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/
```
Associated Topics:
Elementary Puzzles
Elementary Two-Dimensional Geometry
High School Euclidean/Plane Geometry
High School Puzzles
Middle School Puzzles
Middle School Two-Dimensional Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search