New Wikipedia sized proof explained with a puzzle

A new mathematical proof was in the news this week, which partially solves the Erdos Discrepancy Problem. The proof was described as "bigger than Wikipedia". I attempt to explain the problem using a puzzle which you can try at home.

The puzzle was my idea to explain it to you - that's not really how the problem is stated.

New Scientist: http://www.newscientist.com/article/d...
The Independent: http://www.independent.co.uk/life-sty...

Tim Gowers Blog: http://gowers.wordpress.com/2014/02/1...
PolyMath Project: http://michaelnielsen.org/polymath1/i...

The paper: http://cgi.csc.liv.ac.uk/~konev/SAT14...
Boris Konev's webpage: http://cgi.csc.liv.ac.uk/~konev/SAT14/

One page proof that a sequence of twelve has discrepency of 2 http://www.dpmms.cam.ac.uk/~ardm/erdo...