MathDB
rectangular grid , village of pile-built dwellings on a lake

Source: ITAMO 1999 p5

January 25, 2020
combinatoricsgrid

Problem Statement

There is a village of pile-built dwellings on a lake, set on the gridpoints of an m×nm \times n rectangular grid. Each dwelling is connected by exactly pp bridges to some of the neighboring dwellings (diagonal connections are not allowed, two dwellings can be connected by more than one bridge). Determine for which values m,n,pm,n, p it is possible to place the bridges so that from any dwelling one can reach any other dwelling.