Past exam of the options II course of the University of Oxford / 2007 / P / P4 / d / Solution

The transpose has first radius $1/4$, interior radii $1/4+ϵ$, and last radius $ϵ$. These discs are again disjoint and each has one eigenvalue. Intersecting with the previous enclosures therefore improves the last bound toThe identification with the same last eigenvalue is justified by separation from all the other integer-centred discs.