# Sunday Times Teaser 3153 – Pole Position

*by Stephen Hogg*

#### Published Sunday February 26 2023 (link)

Jeb’s 25x25km square ranch had his house’s flagpole at the ranch’s pole of inaccessibility (the point whence the shortest distance to a boundary fence was maximised).

At 50, Jeb gave each of his four sons a triangular tract of his land, with corners whole numbers of km along boundary fences from each corner post (as illustrated, not to scale). Each tract’s area (in square km) equalled that son’s age last birthday (all over 19, but under 30). All the tracts’ perimeters differed, and each son set his hacienda’s flagpole at his own tract’s pole of inaccessibility.

Curiously, for Jeb’s new octagonal ranch the pole of inaccessibility and the shortest distance from this to a boundary fence were unchanged.

Give the eldest son’s shortest distance from his flagpole to a boundary fence.