MathDB

There is a village of pile-built dwellings on a lake, set on the gridpoints of an

m \times n

rectangular grid. Each dwelling is connected by exactly

p

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, p

it is possible to place the bridges so that from any dwelling one can reach any other dwelling.

5

Problems(1)