singingbanana's video: Building Houses Solution

Problem video http://www.youtube.com/watch?v=YMkziQhJkmM Imagine the line from 0 to 1. Write a sequence of points such that the first two points occupy different halves, the first three occupy different thirds, the first four occupy different fourths, and so on. What is the longest sequence you can write? Building Houses game by Christian Perfect: http://christianp.github.io/building-houses/ Follow Christian Perfect on twitter https://twitter.com/christianp Two proofs of the irregularity of distributions (18 point problem) are listed below. But be warned, neither of them are particularly easy reads. First is the proof as demonstrated in this video: Warmus, M. "A Supplementary Note on the Irregularities of Distributions." J. Number Th. 8, 260-263, 1976. http://bit.ly/1j7vgcR Second is a different proof which uses Farey sequences: Berlekamp, E. R. and Graham, R. L. "Irregularities in the Distributions of Finite Sequences." J. Number Th. 2, 152-161, 1970. http://www.sciencedirect.com/science/article/pii/0022314X70900156