TITLE: What is the minimum N for which there exist N points in the plane that cannot be covered by any number of non-overlapping closed unit discs?
QUESTION [19 upvotes]: This problem was posed in March 2010 at G4G9 in a talk by the Japanese mathematician Hirokazu "Iwahiro" Iwasawa. He claims there is a simple proof that N > 10, though he did not share it with the audience, since it proving it is apparently an enlightening exercise in its own right.

REPLY [7 votes]: In the answer to Open problems in Euclidean geometry? , 
Alexey Ustinov brings into attention to a 2012 article. 

Greg Aloupis, Robert A. Hearn, Hirokazu Iwasawa, Ryuhei Uehara, Covering Points with Disjoint Unit Disks, 24th Canadian Conference on Computational Geometry (2012)

The abstract of that article confirms that it's concerned of the same problem, and gives improved bounds.

We consider the following problem. How many points must be placed in the plane so that no collection of disjoint unit disks can cover them? The answer, k, is already known to satisfy 11 ≤ k ≤ 53. Here, we improve the lower bound to 13 and the upper bound to 50. We also provide a set of 45 points that apparently cannot be covered, although this has been determined via computer search.

The article also claims that the lower bound of 11 was published in 2008