2014 IMO Problems
Problem 5
For each positive integer 
, the Bank of Cape Town issues coins of denomination 
. Given a finite collection of such coins (of not necessarily different denominations) with total value at most 
, prove that it is possible to split this collection into 
or fewer groups, such that each group has total value at most 
.
Problem 6
A set of lines in the plane is in 
if no two are parallel and no three pass through the same point. A set of lines in general position cuts the plane into regions, some of which have finite are; we call these its 
. Prove that for all sufficiently large , in any set of lines in general position it is possible to colour at least 
of the lines blue in such a way that none of its finite regions has a completely blue boundary.
