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

[Grapefruit]

27594
This seems impossibly high so I guess at
6939 trade routes

[Sir Colchian Niveus]

If i had Excel from Microsoft Office i could find the solution for you guys.. Do we know when the result will be announced?

[Captain dungeness]

I'm planning on announcing in 1 week from today.

[Sir Colchian Niveus]

Then i'll grab a lot of paper and a bounce of pencils and give it, to you..!

2.097.152 results, is hard to record them..

[Sir Colchian Niveus]

that means to write 2.097.152 results * 21 times... no way dude.. i give up!

[DezNutz]

Base information:
21 Ports Total.
3 Ports for each of the 7 Resources (Excluding Gold).

Explanation of port reference:
The numbers 1-21 each represent a distinct port.
I will group each resource by 3 ports. So ports 1, 2, & 3 will represent resource 'A' and ports 4, 5, & 6 will represent resource 'B", etc. etc.

2 Port Trade Routes:
Starting out your first 3 ports will each have 18 unique routes. 21 minus 3 (Can't trade to same port, and can't trade resource to different port with same resource).
Port 4-6 will have 15 unique routes. 21 minus 6 (3 from Resource A's unique routes (1-4 is the same as 4-1, etc.) and 3 for Same Resource)
Ports 7-9 will each have 12 unique routes. 21 minus 9 (3 from Resource A unique routes, 3 from Resource B, 3 for Same Resource)
Ports 10-12 will each have 9.
Ports 13-15 will each have 6.
Ports 16-18 will each have 3.
Ports 19-21 will each have 0 (all applicable routes will be covered)
This brings the grand total of 2 port unique routes to 189.

3 Port Trade Routes
For 3 port routes, all 21 ports start each with 18 possible base routes. This is due to the 3rd port, as trade route for port 1-4-7 is not the same as 4-1-7.
Now we get to the good part. The 3rd port of the route can be any of 17 possible ports (Can't be starting port as this effectively makes it a 2 port route, and you can't send to a port of the same resource type). It is 17 instead of 15 because the trade routes of 1-4-2 and 1-4-3 are unique, even though the 1st and 3rd ports are of the same resource, due to price variances between ports.

To calculate the possible routes, it is simple math. 21 Starting ports multiplied by 18 possible base routes multiplied by the 17 possible variation for each base route. (21 x 18 x 17)

This brings the grand total of 3 port unique routes to 6426.

4 Port Trade Routes
For 4 port routes, all 21 ports start each with 18 possible base routes. The 3rd port can be any of 18 possible ports (Can't be the same port or resource as port 2). The 4th port can also be any of 18 possible ports (can't be the same port or resource as port 3). Before I go any further, I'm fully aware that the way that the counts for 4 Ports will technically include 2 ports. In fact it will actually count 2 ports twice in the counts due to the inverses of such 1-4-1-4 and 4-1-4-1 which are the same trade route. The total possibles section below will explain it further.

To calculate the 4 port routes, again simple math. 21 Starting ports multiplied by 18 possible base routes multiplied by the 18 possible variation of the base for port 3 multiplied by the 18 possible variation of the port 3 base for port 4. (21 x 18 x 18 x 18)

This brings the grand total of 4 port "unique" routes to 122472.

Total Possible Trade Routes
Sum of 3 Port Trade Routes and 4 Port Trade Routes Minus the 2 Port Trade Routes to counter the duplicate 2/4 Port Trade Routes within the 4 Port Trade Routes. (6426 + 122472 - 189)

Total Unique Trade Routes within Pirates Glory is 128709.

[John jacob astor]

Here is my guess:

2 port trade routes = 189.
3 port trade routes = 5670.
4 port trade routes = 102,060.


TOTAL DISTINCT TRADE ROUTES = 107,919

(And I am sticking with this answer!!)

[Haron]

Nice post Slindur and Haron.
I agree with 1 assumption but not another:

I agree that 3-port routes: 21 options, then 18 options then 15 options (because going to the same resource as the first port would be 'invalid'.
But for 4-port routes there are: 21 options, then 18, then 18, then 15 (an example is Goroum-Hannes-Goroum-Pania 1-2-1-3) the last port can't be the same resource as the first or third port's resource but the 3rd port can be the same as the first resource.

You're wrong about the 4-port routes, Dungeness. And I'm not guessing the answer, I'm STATING the answer Since so many seem to get this wrong, let me elaborate. This'll probably be too much text, but it seems a lengthy explaination is needed. I'll refer to my previous post to keep it shorter.

It seems most people understand that there are 21 options for the first port and 18 for the second. Good. Now, Dungeness stated that there are also 18 options for the third port. That is true, in a way. And you'll see that I have counted all 18 in my post - 15 in the first segment, the same 2 others in segments 2 and 3, and the 18th in segment 4. Why separate them? There are two reasons: 1) The number of legal ports in port four depends on the type of port three. 2) We must remember to remove duplicates. Different segments have different number of duplicates.

OK, first part first - number of legal ports in port 4 as a consequense of the type of port 3 (ignoring that duplicates must be removed). If the third port sells same good as port 1, there are 18 legal ports for port 4. However, if port 3 sells a different kind of good than port 1, there are only 15 legal options for port 4. Thus, we have to distinguish between these cases. In my segment 1, port 3 sells a different kind of good than port 1, and there are 15 legal options for that.

Now to the second part - removing duplicates. I said that if port 1 and port 3 sell different goods, there are 15 legal ports for port 4. Yet, in my segment 1, I only included 12 of them, specifically, those 12 ports that does not sell the same good as port 2. Why? This is to avoid duplicates. Let's see what happens if I let port 4 sell the same good (good A) as port 2. The ports then become: B, A1, C, A2. Note that this is a duplicate of A1, C, A2, B, which appears in later segments. I therefore have to leave those out. When two ports sell the same good, I make sure that is always port 1 and 3, to avoid duplicates. The only situation where I let port 2 and 4 sell the same good, is when port 1 and 3 ALSO does so (segment 3). So, in segment 1, I only allow the 12 ports selling a different good than the 3 first ports. I get quadruples since I get the same trading route starting in any of the four ports of the trading route, so I must divide my answer by 4.

That (segment 1) takes care of 15 of the possible ports for port 3. Now I look at the last 3. One is the same port as port 1, I look at that separately (segment 4). The remaing 2 I ALSO have to look at differently. Why? Because of duplicates. In segment 2, I let port 4 sell a different good than port 2. In this case, I only get pairs of identical trading routes (A1, B, A2, C - A2, C, A1, B) because I have made sure that only ports 1 and 3 can sell the same good, so I must divide my answer by 2. In segment 3, I let port 4 sell the same good as port 2 (yet it cannot BE the same port as port 2, because that would make it a duplicate of my segment 4). It so happens that A1, B1, A2, B2 generates quadruples (any of the four ports can be the first port), so I must divide my answer in this segment by 4. The reason for distingusihing between segment 2 and 3 was therefore becasuse I knew I had to divide by different numbers.

The 4th segment has port 1 and 3 be identical. This is an easy case; port 2 can be any of the 18 selling another good, and port 4 can be any of the 17 others selling another good than 1. It can't be the same as port 2, because that would give A, B, A, B, which is a duplicate of 2-port trading routes. This segment produces pairs of identical routes (A, B, A, C vs A, C, A, B), so I must divide by 2.

I hope I made it clearer, and not harder, to understand

[Most Lee Harmless]

okay, spanner in works time : as you can set the trade route to store any goods into a fleet, not just the 'port goods', should routes between ports producing the same goods be disqualified, as a meaningful trade route can be established using that feature?

[PhoenixKnight]

OK. I finished checking my code results.

for 2p routes, I eliminated same product ports, reversed routes and same port which resulted in 189 unique routes
for 3p routes, I added the condition that port C is not the same as A or B and produces neither products. resulting in 1890 unique routes.
for 4 p routes, I changed port C conditions to be different from port B and produces different product. Hence, port A can appear again. I then added port D conditions to exclude being the same as any of the previous 3 and produces different product than A and C. This gave 27,210 routes.

So 2p=189
3p=1890
4p= 27210

Total of 29298 unique routes.