[Guest]

I had been pondering this riddle for a few days before my friend explained it to me. It's not impossible, you just need to think outside the box a little. Here goes:

How is it possible to plant four trees so that the distance between any two given trees is the same for any pair of trees. That is, if the distance between tree A and B was three feet, the distance between B and C, C and D, D and B, etc. would all be three feet.

If no one gets it for a few days I'll go ahead and post the answer. Have fun!

[itachi-san]

plant 3 trees in a triangle and plant the 4th tree elevated in the center

[Guest]

plant 3 trees in a triangle and plant the 4th tree elevated in the center

Right. I feel bad that this took me so long...

[Guest]

Adding on to Itachi-San's answer:

I believe, if I did my algebra right, that it would have to be (distance)x(square root of 6)/3 feet off the ground.

So, if all the trees are supposed to be 3 feet apart, then the last tree should be 3 times square root of 6 divided by 3 feet off the ground, or about 2 feet, 5.4 inches.

Of course, that height could either be above ground OR below ground (dig a hole).

[Guest]

I had been pondering this riddle for a few days before my friend explained it to me. It's not impossible, you just need to think outside the box a little. Here goes:

How is it possible to plant four trees so that the distance between any two given trees is the same for any pair of trees. That is, if the distance between tree A and B was three feet, the distance between B and C, C and D, D and B, etc. would all be three feet.

If no one gets it for a few days I'll go ahead and post the answer. Have fun!

do you plant them pyramidally?

[Guest]

What if the question was expanded to state that all of the trees needed to be planted at "surface level"?

[Guest]

some alternate universe with weird measurements

[Guest]

Place 3 of the trees in an equilateral triangle pattern at grade level, then place the fourth tree in the center of the triangle with a hypotenuse distance equal to the length of one of the sides either above or below grade

.. there ya go

Edited May 21, 2008 by Thoth

[Guest]

What if the question was expanded to state that all of the trees needed to be planted at "surface level"?

Imagine a tetrahedron (a pyramid of 4 equilateral triangles) inside the earth with the 4 corners just reaching the surface. Plant the trees at each of the four corners.

[Guest]

Has anyone thought about planting them in a square? <_<

[Guest]

Has anyone thought about planting them in a square? <_<

That is what i thought

[Guest]

To explain why a square doesn't work...

A visual representation where the trees are 1, 2, 3, 4:

1------2

-

-

3------4

Pretend that that is a square. 1 and 2 are closer together than 1 and 4.

(The distance between 1 and 4 is d=sqrt(2*x^2), where x is the distance between 1 and 2. Simplified, d=x*sqrt(2). Since the square root of 2 is about 1.4, the diagonal is 1.4 times longer than the side.)

All pairs of trees had to be the same distance apart.

Edited May 21, 2008 by Dragonjest22

[Guest]

'Planting' could include seeds which could easily be in a triangular pyramid configuration or touching eachother.

Edited May 21, 2008 by dave273

[Guest]

Planting the trees on a hill with one at the peak gets over the problem of all trees to be planted on the land surface. Choosing the correct shape of hill is very important as we must also consider the distance between each pair of trees at the closest point which may be anywhere between the top and the bottom.

[Guest]

That is what i thought

That is waht i thought

[Guest]

Has anyone thought about planting them in a square? <_<

I dont think that would quite work, so you have them in a square with equal distances to each in at 90 deg angles, thats ok, however the corner trees are not the same distance apart from the opposite corner

[Brandonb]

I dont think that would quite work, so you have them in a square with equal distances to each in at 90 deg angles, thats ok, however the corner trees are not the same distance apart from the opposite corner

*this is just a secondary thought, I realize that it's not the intentional answer, but it works.

Unless the foliage on the trees has been sculpted into squares, then the trees could be arranged in a square, each with two sides touching and each having a corner touching the other three trees. Of course that doesn't apply to the bases of the trees.

For the bases of the trees, they could be grown in square molds, and planted in the same fashion as the previous explanation. Though it's really not possible to plant trees that close together in reality without them growing together.

...you said outside the box

[Guest]

Take a cube-shaped box of soil. Make a hole in one corner of the box and plant a seed in it. Mark the 3 adjacent corners so you don't plant a seed in those. Then plant a seed in the 3 corners which are adjacent to those. So a tree will grow out of every other corner of the box. That's four equidistant trees. That way you can do it without thinking outside the box!

[Guest]

Distance = 0

[Guest]

I haven't read anybody else's answer, so forgive me if I'm just repeating things.

If you planted them on a tetrahedral hill, with three at the base and one on top, all four trees would be equidistant, as measured from their bases.

[Guest]

or...

plant three at 30 degrees latitude, 60 degrees apart, and one at the North pole.

[Guest]

it seems strange why you would want to do that. i would just plant the trees in a nice straight row.

[Guest]

You all got way "out of the box" here, but then again, .... it took me forever to realize that such things as hills exist in the world. *headdesk*

[Guest]

it seems strange why you would want to do that. i would just plant the trees in a nice straight row.

I'm sure that would look very nice, and be easy to water and harvest, but it doesn't solve the OP, because all 4 must be equidistant from every other tree. In your solution, the tree on either end would be 3 times as far from the tree on the opposite end as it is from the tree right next to it. If I just had four trees to plant, and could do it however I wished, I would also plant them in a nice straight row. Possibly next to a shrubbery.

[Guest]

make a triangle-based pyramid (a pyramid that has four sides)

[Guest]

TRIVIA

Trouble with trees is they grow at different rates, so it won't last for too long.

Plants are like people - they are individual and unpredictable to a degree where variables can not be calculated.