Red points
Erich Friedman is a math professor and puzzle enthusiast. Red points is his own creation. Colour five of the points in the image above red in such a way that the distance between any two of them them are all different. That is ten distances, by the way.
Here, is an example:
December 4th, 2007 at 10:23 am
Letter the columns a-e and number the rows 1-4 (1=lowest) as in chess.
A 4×4 square provides only 9 different positive distances, exemplified by (1, 0), (1, 1), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1), (3, 2), (3, 3). Thus both the a- and the e-columns contain at least one red point. Beyond that, I can’t see any short cuts, and the problem is one of brute force (e.g. depth-first search), and for me it isn’t fun any more.
The matter doesn’t crop up with such a small array, but, with big enough arrays, beware that a1 is the same distance from e4 and f1.
(BTW, this set of 5 works: a3, a4, c4, d1, e2.)
December 4th, 2007 at 12:41 pm
This picture (if the img tag works right) shows the distances between each point. Should help. =)