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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 3030 square rooms situated like the cells of a 2×152 \times 15 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?