Two hundred forty-five

What this map does not hide

The country is the grid

All 254 district boundaries were read — 4,506 exterior rings, 1.2 million points — and a hexagon cell counts as land when its centre falls inside one of them. That is 229 cells, plus 13 added at their own position for districts whose island is smaller than a single hexagon: 242. Then the part that matters: no district crosses water. The mask is split into connected components first — mainland, Ulleung, Ongjin, Geoje, Jeju — and a district belongs to the one nearest its centroid. A component with cells to spare drops the ones furthest from any district; one that is short grows toward the districts that want in. Jeju gave up two of its four, the mainland gained five, and 245 cells hold 245 districts with none left over. Inside each component the Hungarian algorithm on squared distance settles the rest, so it is the optimal arrangement rather than a greedy one. Nothing was placed by hand and a rerun produces the same file.

Tiles are displaced

Mean displacement is 1.81 cells, about 43 km; the worst is 5.01 cells, 137 km. All eight of the worst are Hanam, Guri, Seongnam Jungwon, Gangdong, Seongnam Bundang, Gwangju, Yangpyeong and Jungnang — the ring east of Seoul, where districts are packed tightest. That is not a failure of the fit, it is what a cartogram is. One hexagon per district gives every district the same area, so the capital region must take more of the picture than it takes of the land, and something has to move. Before districts were stopped from crossing water, Wando and Jindo sat beside Jeju: nothing was wrong with their centroids, but Jeju had more cells than districts, the surplus had to be filled, and the two nearest candidates were taken. A global optimum over the wrong feasible set is still the wrong answer.

Eleven are absent

The boundary file is 2023 and the population and brokerage files are 2026. In between, Hwaseong split into four wards, Incheon reorganised into five and Cheongju into two. No 2023 centroid exists for a district created in 2024 — Hwaseong’s Dongtan, Manse, Byeongjeom and Hyohaeng; Incheon’s Geomdan, Michuhol, Seohae, Yeongjong and Jemulpo; Cheongju’s Seowon and Cheongwon. They are named rather than invented.

There are no labels

Names do not fit on 245 hexagons. This map answers "where is the rate high", not "what is Sejong’s rate". Names and numbers appear in a popup on hover. The popup needs JavaScript; with it off, the browser’s own tooltip gives the same name and rate. For anyone who has neither, the full list in rank order is below.