How many possible trade routes contest. 15M gold prize!

[Most Lee Harmless]

the port cannot trade with itself : so its 20 x 20 = 400/2 (to remove reverse routes) = 200 unique and unrepeated routes

Port 1 can go to 20 other ports
Port 2 can go to 19 other ports ( as it already has a route to 1)
Port 3 can go to 18 other ports ( as it already goes to 1 and 2)

and so on, each new port has 1 fewer route it can do without repeating prior ones.

by port 21, all that is left is itself, which it cannot go to.

[Brazzler]

love how much arguing is going on here. It's just a game people!

[Haron]

The "reverse trading routes are excluded" caused a little more trouble than it should have. I failed to see that the 4 port trading routes with 2 identical ports (A-B-A-C) didn't have a "reverse" the way I counted them. To avoid the mess of my earlier posts, here goes again:

2 ports: 21*20/2 = 210
3 ports: 21*20*19/3 = 2660. Removing reverse routes: 1330
4 ports (all different): 21*20*19*18/4 = 35910. Removing reverse routes: 17955
A-B-A-C combos: 21*20*19/2 = 3990 (here, I've assumed that the port visited twice always comes first, so no reverse routes has to be removed, as they were never counted, and shouldn't be counted, as A-B-A-C is identical to C-A-B-A).

Total: 23485

Not removing reverses (which gives the TRUE value for unique trading routes): 42770

Counting ALL permutations as equal (again, wrong, but I suppose some might think this is a good idea for some reason)

2 ports: 21*20/2 = 210
3 ports: 21*20*19/6 = 1330
4 ports (all different): 21*20*19*18/24 = 5985
A-B-A-C combos: 21*20*19/2 = 3990

This gives a total of 11515.

So, the number of unique trading routes REALLY is 42770, but the question as stated (removing reverse trading routes, but not ALL permutations) gives the number 23485. Counting ALL permutations as "identical" would give 11515.

And brazzler: Did you say "JUST a game"?!? *shudder*

[Most Lee Harmless]

sorry to add more complications but it seems 1-2-3-4 and 2-3-4-1 are considered as the same sequence ; which would also then include 3-4-1-2 and 4-1-2-3 (plus reverses) : that would make figuring out the 'unique 'sequences a real pain.

[Haron]

That's included in my calculations, Danik. That's why I divide 2 port routes by 2 (can start at any of the two ports), 3 port routes by 3 (can start at any of the 3 ports) and 4 port routes (consisting of 4 different ports) by 4 (can start at any of the 4 ports). This takes care of 1234 = 2341 = 3412 = 4123.

[Most Lee Harmless]

Ah, thankee for the clarification

[Grimrock Litless]

21 + 20 + 19 + 18 + 17 + etc...

I would say 231 able trade routes.

Haven't read the rules yet.

7 + 6 + 5 + 4 + 3 + 2 + 1

5 + 4 + 3 + 2 + 1

Total of 274 as the limit is 4 port trade routes.

Could be wrong.

What are unique trade routes?

[Captain Jack]

That's an interesting one to watch. I must add that we never calculated this metric but it would be nice to have it

[Grapefruit]

Each port cannot trade with 20 other ports as two of those ports sell the same product.
Goroum cannot trade with New Land as they both sell food.

[Most Lee Harmless]

Oh, that's an excellent point!