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

[Most Lee Harmless]

1-2-1-3 is the same as 1-2 AND 1-3 : the route will already exist from the basic pairs derived from your 21 destinations : if port A and B are already connected by a previous route, then it dont matter where the ship came from to reach A or where it went after B : its the pre-existing route between them that disqualifies any other combination that includes them.

I'm not saying that is logically correct : but according to the conditions given by Captain D, no other outcome is logically possible.

Your calculation is based on : how many 2 unique port combinations are there : PLUS : how many unique 3 port combinations are there : PLUS : how many unique 4 port combinations are there : DISREGARDING : reverse routes or repeated sections of routes.

But that is not the stated conditions of the OP.

[Haron]

How can a fleet have BOTH trade routes 1-2 AND 1-3? It has to have EITHER 1-2 OR 1-3. And therefore, 1-2-1-3 is a unique trading route. And if I have only one fleet, I might like to set up such a route for example to stock ship building supplies from 2 and 3 in port 1.

Saying that "1-2-1-3 is the same as 1-2 AND 1-3" doesn't make sense to me. The only way you can get a fleet to traverse these ports in that order, is by setting up that trading route. You can NOT achieve such a route by going 1-2 (repeat), nor can you achieve it by going 1-3 (repeat).

[Admiral Nelson]

I have not read through it properly.

But has anyone remembered the store in warehouse 1/2 or both trade route?

[Most Lee Harmless]

How can a fleet have BOTH trade routes 1-2 AND 1-3? It has to have EITHER 1-2 OR 1-3. And therefore, 1-2-1-3 is a unique trading route. And if I have only one fleet, I might like to set up such a route for example to stock ship building supplies from 2 and 3 in port 1.

Saying that "1-2-1-3 is the same as 1-2 AND 1-3" doesn't make sense to me. The only way you can get a fleet to traverse these ports in that order, is by setting up that trading route. You can NOT achieve such a route by going 1-2 (repeat), nor can you achieve it by going 1-3 (repeat).

If '1-2' precludes 'any combination of 2 and 1 : and '1-3' precludes any combination of 1 and 3 : then between them, they preclude any combination of 1, 2 and 3 : if 1-2, 1-3, 2-3 already exist as pairs, they block any further use of those pairs in any other route. Same applies to 1-4, 1-5, 1-6, 1-7, 1-8 all the way to 1-21.

I did say it was not logical : but it is logical within the conditions stated by Captain D : that's the catch :

[Haron]

But 1-2 does NOT preclude any combination of 2 and 1. How can you read the post in such a way? Surely, 1-2-3 is a unique trading route, distinct from 1-2, from 2-3 and 3-1? I think you read things into the post that isn't there. 1-2 only precludes any routes giving the same result as 1-2, like 1-2-1 and 1-2-1-2.

Also the "a reverse trading rout is a duplicate" bit should not have been in the post, in my opinion, since A-B-C and C-B-A clearly are different trading routes, giving different results, but that is another matter.

[Most Lee Harmless]

'1-2' precludes 1-2-1, for example.. because the element '1-2' already exists : if that is so, then 1-2-3 must be excluded on the same basis : '1-2' already exists. What the fleet does before or after the element '1-2' (or its reverse) becomes irrelevant. if 1-3 exists as a unique pair, then a route containing 1-3 (or its reverse) is excluded on the same basis. If 1-2 and 1-3 already exist, then ANY combination of routes that include either (and/or their reverses) must be excluded.

If the conditions were 'how many unique 4 port combinations are there' : then your argument is valid, but that is not the condition ( and example) given by the OP.

[Haron]

1-2 precludes 1-2-1 BECAUSE THEY ARE IDENTICAL. 1-2-1 = 1-1-2 = 1-2. Just set up the #&¤%"#¤ trading routes and see for yourself. It is NOT because 1-2 is PART of 1-2-1. THEY ARE IDENTICAL. 1-2-3, however, INCLUDES 1-2, but is not IDENTICAL to 1-2, so it has to be included.

It is not stated anywhere that the route 1-2 precludes any route containing the part 1-2, like 1-2-3. That would have been a really stupid rule.

(Well, so is the actually stated rule about reverse trading routes, so I guess "that would have been stupid" is not really a good argument...)

[Most Lee Harmless]

I agree, it is odd : I did say it was not logical : but the competition has created exclusions, and if one follows the exclusions to their logical conclusion then no 3- or 4- port combination can exist within those terms.

[Haron]

I disagree about what you get by "following the exclusions to their logical conclusion". It is said that DUPLICATES are to be removed, and then 1-2-1 is given as an example of a duplicate of 1-2. Which is to say, they are identical, and should therefore only be counted once. It does not say anywhere that routes containing 1-2, which are NOT duplicates (like 1-2-3), should be removed.

Then, separately, the post states that reverse trading routes are excluded. So, he wants the number of unique trading routes minus those that have a reverse trading route that is not also a duplicate.

[Sir Sam Lowe]

Delrio's Trade Theorem

Each route has 20 other routes

To each trade route;20 is equal to the amount of options for each

As a result of my bad math skills I would say 420.

But for each route you would have to eliminate a duplicate so;

Ans=210

____________________________________________________________________________________________________________________________________________________________

Formula

The amount of objects multiplied by it's possible outcome s
Divided by 2;to eliminate all duplicates.
The answer you get should be correct
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Worksheet

20 x 21=420

420

2

Ans:210