by Nick MacKinnon
Published: 12 February 2017 (link)
King Lear IV’s realm consisted of a regular hexagon divided into 24 counties that were equal-sized equilateral triangles. In his will he wanted to share the counties among his six daughters, each daughter’s portion having the property that, if you walked in a straight line between any two points in it, then you remained in her portion. If two daughters’ portions had the same area then they had to be of different shapes (and not the mirror image of each other). He wanted Cordelia to have a single county (his favourite county on the edge of the kingdom), he wanted Goneril to have a hexagonal-shaped portion, and he knew the number of counties he wanted to allocate to each of the other daughters, with Reagan’s portion being the largest of all. It turned out that his requirements uniquely determined Goneril’s and Reagan’s counties.
What, in increasing order, were the numbers of counties allocated to the six daughters?