I simply could not understand the point of this puzzle, as it stands. The "cities" should be at the vertices of a quadrilateral, of course --- what else is a solver supposed to deduce? The distances given are presumably (very) approximate --- if they were exact, the landscape would have to occupy hyperbolic space. [The enclosed "tetrahedron" --- which should be flat --- actually has imaginary volume approximately \iota.] If you're setting a puzzle based on this idea, why not put some work in and base it on a matrix of exact integer distances in the Euclidean plane? A candidate with small lengths, which avoids any simple parallelograms, would be 8 4 4 6 7 8 Perhaps the final distance might be omitted, and the solver challenged to find it. [Some side condition would be needed to exclude the other, shorter, possible solution.] Even then, elementary dexterity with a pair of compasses would in practice reveal the answer in a few seconds! Fred Lunnon On 11/26/06, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
In my latest large update (http://www.mathpuzzle.com/ ), I give a problem based on ambiguously placed cities. You are given straight line distances between cities A, B, C, and D. Can you make a map of where the 4 cities are, in relation to each other?
D C B A | 3.10 7 5 B | 5.44 3 C | 6
I show a diagram at my site, along with 16 other recreational math items that have come to my attention.
Ed Pegg Jr http://www.mathpuzzle.com/
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