Planting TreesDate: 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/ |
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