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 Landscape Architect (Posted on 2003-09-27)
You are working as an apprentice to a landscape architect. Your first assignment is to plant some trees in a client's large, flat lawn. Your boss tells you:

"I want you to plant 16 trees in 15 rows. There must be exactly 4 trees in each row."

How should you plant the trees if you want to complete your assignment?

 See The Solution Submitted by nikki Rating: 3.2500 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 6 of 9 |
To position the trees, draw a star, placing ten trees on each point and corner.
Then, draw a star inside that, using the inside 5 corners as the second star's outside points, and place five more trees on the inside corners of the smaller star. Place the final tree in the center.

The outside star provides five lines:
```

·

*             *           *              *

·

·       ·

·

·      ·     ·     ·

·

·                         ·

----------------------------------------------------

*

·             *           ·              ·

·

·       ·

·

*      ·     ·     ·

·

*                         ·

----------------------------------------------------

*

·             ·           *              ·

·

·       ·

·

·      ·     ·     *

·

·                         *

----------------------------------------------------

·

*             ·           ·              ·

·

·       ·

·

*      ·     ·     ·

*

·                         *

----------------------------------------------------

·

·             ·           ·              *

·

·       ·

·

·      ·     ·     *

*

*                         ·

```

Similarly, the edges of the smaller star make up five more lines:

```

·

·             *           ·              ·

·

*       ·

·

·      *     ·     ·

*

·                         ·

----------------------------------------------------

·

·             ·           *              ·

·

·       *

·

·      ·     *     ·

*

·                         ·

----------------------------------------------------

·

·             ·           ·              ·

·

·       ·

·

*      *     *     *

·

·                         ·

----------------------------------------------------

·

·             ·           *              ·

*

*       ·

·

*      ·     ·     ·

·

·                         ·

----------------------------------------------------

·

·             *           ·              ·

*

·       *

·

·      ·     ·     *

·

·                         ·

```

That's ten out of the fifteen.
Up to this point we haven't used the center tree yet. The last five rows each utilize the center tree along with one tree from each of the four concentric pentagons we have formed. The trees are not evenly spaced, but they are in a straight line (don't trust my drawing, but they are):

```

·

*             ·           ·              ·

·

*       ·

*

·      ·     ·     *

·

·                         ·

----------------------------------------------------

·

·             ·           ·              *

·

·       *

*

*      ·     ·     ·

·

·                         ·

----------------------------------------------------

*

·             ·           ·              ·

*

·       ·

*

·      ·     ·     ·

*

·                         ·

----------------------------------------------------

·

·             ·           *              ·

·

·       ·

*

·      *     ·     ·

·

*                         ·

----------------------------------------------------

·

·             *           ·              ·

·

·       ·

*

·      ·     *     ·

·

·                         *

```

So, that's it, 15 rows from 16 trees.
Edited on September 28, 2003, 2:32 am
 Posted by DJ on 2003-09-28 02:24:19

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