Trees

Our four Scribes, having this time made sure that everyone has his fair share of larma fruit, are discussing peculiarities that they have seen during the preceding year, when a passing Builder interrupts their conversation.

“Here’s a novelty for you,” he says. “In my gardens, which are reasonably extensive, I have had four Ka-la-na trees planted exactly a tenth of a pasang apart. And by that I mean, each of the four is exactly a tenth of a pasang from each of the other three.”

He looked expectantly at the Scribes, but Plato for one had no intention of being satisfactorily nonplussed. “Ingenious,” he said approvingly. “I suppose you…?” And he outlined a method of planting the trees.

The Builder, with a mixture of amusement and annoyance, said, “No, although I see that would have worked.”

“Then in that case,” Socrates chimed in, “I imagine you…?” And he outlined another method.

Seeing the Builder shake his head, Aristotle said “Perhaps what you did was…?”

His suggestion was also wrong, although yet again the Builder had to admit that it would have been perfectly feasible, and Diogenes then came up with the correct arrangement.

How is it possible for the Builder’s garden to feature four Ka-la-na trees, each of them a tenth of a pasang from all three of the others?