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 starting from home, the volunteer next is to make pickups for the shelter at the supermarket and the bakery (in either order), the first two intermediate points on his route, beginning with the first must be..
- $1$ and $2$
- $1$ and $3$
- $2$ and $1$
- $2$ and $4$
- $4$ and $2$