Monday, January 22, 2007

A Tough Brainteaser and a Tougher One

Suppose you have ten trees. How can you plant these trees so that they form five rows of four trees each. Leave a comment if you figure out the answer.

If the first problem is tough, the second one is much tougher. How can you you do the same task (plant five rows of four trees) with only eight trees. It sounds impossible, and it is unless you use an imaginative approach. (Hints: Don't bother planting more than four trees in a row. The second problem is possible, but may not be practical.)


Bobby Griffin said...

I figured out the first one...don't really know how to explain it here in the comments though. Still working on the second one.

Daniel Thompson said...

The first problem has at least two solutions. One should be really easy to describe in words. The other one isn't as easy to describe.

The answer to the second problem should be explainable in words, it just might take a lot of them.

Anna said...

The first one is a pentagonal-star shape - like a pentagram that isn't inscribed in a circle.

The second one - it's "impractical" because it uses the non-euclidian geometry of the globe's shape. You'd have to spread them out over the globe to get them to work.

Daniel Thompson said...

You're correct. Good job!

Pickled Eel said...

* * * *
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Mmm, I wonder if this "graphic approach" will work for the first problem?

Michael-Alapaki said...

The solution to the 10 tree problem is a five pointed star, where the trees are planted at each star tip, and at each intersection.
The solution to the 8 tree problem is to plant the trees equidistant on a globe, such as the earth.
To visualize this, simply draw a cube, plant the trees at each of the 8 corners of the cube. Then imagine those points superimposed on a globe that is centered on the cube.

Anonymous said...

Pretty simple.. arrange them in the shape of a Star.. a pentagonal one