## 27. Pharmacies

New Town contains 13 groups of houses: $a, b, c, d, \ldots$, $l$ and $m$. It is known that $a$ neighbors $b$ and $d; b$ neighbors $a, c$ and $d$; $c$ neighbors $b; d$ neighbors $a, b, f$ and $e; e$ neighbors $d, f, j$ and $l; f$ neighbors $d, e, j$, $i$ and $g; g$ neighbors $f, i$ and $h; h$ neighbors $g$ and $i; i$ neighbors $j, f, g$ and $h; j$ neighbors $k$, $e, f$ and $i; k$ neighbors $l$ and $j; l$ neighbors $k$ and $e$, while the group of houses $m$ is isolated - apart from the other houses.

## 88

Each resident of this new town must have access to a single pharmacy in the nearest vicinity, i.e., in their own group of houses or in one of the neighboring groups. Where should these pharmacies be located?
27. Pharmacies should be located in groups $b, i, l$ and $m$. This is easily discernible from the diagram by representing each group 

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-217.jpg?height=757&width=945&top_left_y=658&top_left_x=561)

of houses with a point and connecting adjacent groups with straight line segments.