How did the tree farmer do this?

Question

A tree farmer plants a total of 10 trees in five rows with four trees in each row. How did he do this?

Answer 1

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.

Answer 2

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