[math-fun] A Property of 17

For a long time, I've been stumped by the following property of 17. This is from David Wells' book, "Dictionary of Curious and Interesting Numbers": 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? Bob Baillie