# Shortest path for delivering packages [duplicate]

This question already has an answer here:

A version of the Travelling Salesman Problem, but with certain points.

We are talking about a town where 8 canals run from the middle boathouse into the city. You can only travel one way on the green canals.

The blue canals lie around the city in a circular shape. On the blue canals, you can travel both ways. You cannot turn half-way the canals, you may turn at a crossing of the canals. All the pieces of green canal have a length of 4, each piece of canal from canal to canal has a length of 3 (inner canal), 6 (middle canal) and 9 (outer canal).

You start at the central boathouse, from there, you need to deliver 6 packages to the red triangles. then, you have to go back to the central boathouse.

What is the shortest length of the route you can take to deliver those 6 packages?

## marked as duplicate by JonMark Perry, Rand al'Thor, boboquack, Quintec, Dr XorileDec 9 '18 at 22:47

• Is it just me, or have I seen this on puzzling.SE before? – Hugh Dec 8 '18 at 17:28
• @Hugh, it looks similar, but as you mentioned, the triangles are moved around and not in a simple rotational manner. will it have different solutions? – SteveV Dec 8 '18 at 18:10
• apparently pi=3 ? :-) – deep thought Dec 9 '18 at 1:38

I think I can do it in

85

by (C = clockwise, R = counterclockwise, I = inwards, O = outwards)

1. OOO (to Z) R (21)
2. IR (10)
3. OC (13)
4. IIRR (14)
5. ROR (13)
6. IC (7)
Finish: CI (7)

I'm not sure if this is optimal but it's definitely close. The only thing that has room for improvement is probably the finish.