Thanks much! Wells' book gave no reference and I had no idea what that problem was called. I'll look up Graham's paper if I can't find it online. Bob --- Dan Asimov wrote:
Robert Baillie wrote:
<< Choose numbers a, b, c, ... in the interval (0, 1) so that a and b are in different halves of the interval; a, b, c are in different thirds; a, b, c, d are in different quarters, etc. Not more than 17 such numbers can be chosen. First, can 17 such numbers be chosen?
Second, why can not more than 17 such numbers be chosen?
17 is in fact the maximum; this result is from a 1970 paper of Ron Graham and Elwyn Berklekamp: "Irregularities in the Distributions of Finite Sequences." J. Number Th. 2, 152-161, 1970.
See also < http://mathworld.wolfram.com/18-PointProblem.html >.
--Dan
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