Question 74
A building has seven rooms numbered $1$ through $7$, all on one floor, and any number of doors connecting these rooms. These doors may be one-way, admitting motion in only one of the two directions, or two-way. In addition, there is a two-way door between room $1$ and the outside, and a treasure in room $7$. Your object is to choose the arrangement of the rooms and the locations of the doors in such a way that
a. it is possible to enter room $1$, reach the treasure, and make it back outside,
b. the minimum number of steps required to do this (each step consisting of walking through a door) is as large as possible.
a. it is possible to enter room $1$, reach the treasure, and make it back outside,
b. the minimum number of steps required to do this (each step consisting of walking through a door) is as large as possible.