30 square rooms situated like the cells of a 2x15 board in a rectangle bulding
Source: Austrian - Polish 1994 APMC
May 3, 2020
rectangleSquaresTilingcombinatorial geometrycombinatorics
Problem Statement
A rectangular building consists of square rooms situated like the cells of a board. In each room there are three doors, each of which leads to another room (not necessarily different). How many ways are there to distribute the doors between the rooms so that it is possible to get from any room to any other one without leaving the building?