A volunteer uses a truck to pick up donations of unsold food and clothing from stores and to deliver them to locations where they can be distributed. He drives only along a certain networks of roads.
In the network there are two-way roads connecting each of the following pairs of points. $1$ with $2, 1$ with $3, 1$ with $5, 2$ with $6, 3$ with $7, 5$ with $6,$ and $6$ with $7$. There are also one way roads going from $2$ to $4,$ from $3$ to $2$, and from $4$ to $3.$ There are no other roads in the network, and the roads in the network do not intersect.
To make a trip involving pickups and deliveries, the volunteer always takes a route that for the whole trip passes through the fewest of the points $1$ through $7,$ counting a point twice if the volunteer passes through it twice.
The volunteer 's home is at point $3.$ Donations can be picked up at supermarket at point $1,$ a clothing store at point $5,$ and a bakery at point $4.$ Deliveries can be made as needed to a tutoring center at point $2,$ a distribution center at point $6,$ and a shelter at point $7.$
If the volunteer is to make a trip starting at the shelter, next going to the bakery for a pickup, and then ending at the distribution center, the first two intermediate points on his route beginning with the first can be.
- $3$ and $1$
- $3$ and $4$
- $4$ and $2$
- $6$ and $2$
- $6$ and $5$