An Eccentric Billionaire's Riddle of Fours

May 19, 2008

RAY: This puzzler is from my horticultural and mathematical series. It was sent in by Daniel Reiss. And, of course, I couldn't resist the temptation to mess with it a little bit.

Here it is.

An eccentric billionaire decided to interview landscapers for his newly constructed estate. Part of the interview was a simple test. He said:

"Four is my lucky number. I made my fortune working four hours a week, just like those two knuckleheads on Car Talk!

"So, I want every tree and bush and shrub you plant to be in groups of four. Got it? But in addition, I want each of these four things that you plant, to be the same distance from one another.

"For example, if you plant four rhododendron, I want them all to be equidistant, i.e., each one is the same distance from each of the other three."

The question is, can it be done?
RAY: So here's the answer. Tommy, do you have a clue?

TOM: I do know the answer!

RAY: Yeah, well, you know the answer because you looked over my shoulder. Most people think on one dimension.

TOM: Yes, we do. I'm a one-dimensional kind of guy.

RAY: But for this puzzler, you need three dimensions. So if you'd plant the first three of anything at the three points of an equilateral triangle, you plant the fourth tree on the top of a hill which is precisely in the middle of the three, and it's at a height such that the size of the three new triangles that you make are the same as the original triangle that was made by the first three things that were planted.

TOM: Yes.

RAY: And that's how you get four things that are equidistant.

TOM: It's as high as the distance between any of the other two. Brilliant!

RAY: Bingo! So who's our winner?

TOM: The winner this week is Paul Lucia from Houston, Texas, and for having his answer selected at random from the pile of correct answers that we got, Paul's going to get a 26-dollar gift certificate to the Shameless Commerce Division at, with which Paul can get just in time to re-gift for Father's Day, a copy of our new four-CD Car Talk set called Field Guide to the North American Wacko.

RAY: Congratulations, Paul!

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