# 9 trees in 7 rows with 3 trees in each row

The following puzzle is a variant of a puzzle published in the May 8, 1926 issue of THE WINNIPEG TRIBUNE MAGAZINE:

In the picture below there are nine trees arranged in two rows with five trees in each row. The puzzle is to reposition four of the trees leaving the other trees untouched so that you wind up with exactly seven rows with three trees in each row. Rows can be horizontal, vertical or slanted at any angle.

• I might be the odd one out, but I would argue this puzzle could be improved by replacing the word 'row' with 'line'. Calling two perpendicular lines rows seems weird/confusing to me? Aug 24 at 8:52
• @DavidMulder I am sorry that the word "row" was confusing. However, "row" is the standard word for this type of puzzle (I checked a number of sources). I will update my question. Aug 24 at 9:31
• @DavidMulder A row of trees going north-south is as much as a row of trees going east-west. Aug 24 at 13:12
• @PeteKirkham Taking each row on its own I would wholeheartedly agree, but when you have e.g. a 2x2 grid I would say that that grid has two rows and two columns, not four rows and two columns. And I believe the same would apply to any set/group/collection of rows. Aug 25 at 6:14
• You should clarify exactly 7 rows. My first thought was to arrange in a 3x3 grid.
– qwr
Aug 25 at 14:45

## 8 Answers

A different solution is possible:

• Nice symmetrical solution! Nicely explained too! Aug 24 at 18:24
• Just put them into a 3x3 box at first, then did stuff to get rid of one row. Aug 25 at 14:58

How about the following arrangement?

Made from moving the four trees farthest from the center.

• Yes, that works. Can you find a symmetrical solution? Aug 24 at 0:56
• @WillOctagonGibson Ah, yes, simply shift the top row over by one. I'll edit my answer Aug 24 at 7:42
• This new solution makes 8 rows (not just 7), with the long diagonal from bottom left to top right... (This is also achieved by just positioning the 9 trees in a 3x3 square grid.)
– Stiv
Aug 24 at 7:51
• if you move the left tree in the first row of your original answer down three rows then you get a symmetric solution with 7 rows (and not more)
– daw
Aug 24 at 8:53
• My bad, I'll revert my edit. Aug 24 at 19:50

I'm quite happy with the result, and had fun thinking about it

• I like your symmetrical solution. You explained your answer well. Aug 26 at 2:31
• Very good answer. Aug 26 at 20:39

This doesn't quite follow the rules

but why move 4 trees when it can be done in 3?

Yet another answer. Who said all the trees must be used?

• Cool! Thinking outside of the box! Aug 26 at 2:38
• I like the way you show the original positions of the moved trees here. That's a really good visual representation. Aug 26 at 9:41

I can actually make 9 rows with 3 trees in each row by just moving 4 trees. I will keep the top and bottom tree and the three center ones in place and move the other 4 to build the following pattern (F for fixed trees and M for the ones I moved).

Sorry for not actually having nice trees in my picture. Feel free to edit.

• Ideally I am looking for a solution with exactly 7 rows. Aug 24 at 9:18
• Move the top right M further out along its line and you eliminate 2 rows to leave 7. Aug 24 at 12:32

I'm not sure if this would be allowed, because this solution involves

trees being not exactly grid aligned, and also one row having way different spaceing between trees. Though, I did try to keep the distance within each row the same, because this would be really easy if any adjacent trees in a row can be any distance apart.

• That looks perfectly good to me, except you forgot to draw one line. Aug 27 at 20:40
• @FlorianF That looks like seven lines to me though.. Three horizontal, one vertical, two negative diagonals, and one positive diagonal. Aug 28 at 4:53
• Oops, it seems I cannot count. I saw an additional row from the top left to the bottom right tree, but I didn't see that you moved the bottom right tree to avoid that. So no objection. Grid alignment was not a requirement. Aug 28 at 8:51

Found this one:

Here's how I did it.

• Nice symmetrical solution. Aug 29 at 20:09