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

[Haron]

John Jacob Astor: I know I'm right, because my math is a proof. I've looked at some other tries, and I have no problem pointing out the errors in most of them (I can't explain the error in those who tried using a computer program, though - I don't know their code for removing duplicates well enough). The beauty of a mathematical proof is that you can't really argue with it. You can point out mathematical errors, but if the math is correct, the answer is correct. Also, I showed this puzzle to some fellow mathematicians, who obviously also arrived at the same answer.

Like I always say: There are three kinds of people: Those who know math, and those who don't

[John jacob astor]

well i'll call my answer a proof then too, so now i know i'm right too! let's all just call our answers proofs and the dungeness will have to give us all 30m because we are all right!

[Captain dungeness]

Also, I showed this puzzle to some fellow mathematicians

This is getting exciting!
I am concerned only with arriving at the correct answer, there should be no guessing games on which answer to use- use the right one and we can debate it when the contest ends in a few days.

So far: Shaydo and I both have a list of all possible routes.... unfortunately one list has 11 more than the other and we are trying to determine which routes are different and why.

[Haron]

Dungeness: What program do you have your list in? Excel? Is it possible to post such a list here somewhere? I think finding "illegal" routes and duplicates in a list should be relatively easy. However, pointing out legal routes that are missing from a list is a little more tricky. Doable, but definitely more tricky.

[Admiral Nelson]

[quote="Haron"]Dungeness: What program do you have your list in? Excel? Is it possible to post such a list here somewhere? I think finding "illegal" routes and duplicates in a list should be relatively easy. However, pointing out legal routes that are missing from a list is a little more tricky. Doable, but definitely more tricky.[/quote]

Surely, you are not still arguing about this?

Its kind of sad.

But that is just my perspective.

I do understand, there is 15 Million on the line.

[Captain dungeness]

Dungeness: What program do you have your list in? Excel? Is it possible to post such a list here somewhere? I think finding "illegal" routes and duplicates in a list should be relatively easy. However, pointing out legal routes that are missing from a list is a little more tricky. Doable, but definitely more tricky.

I am using Lua and exporting to a .txt file. It is comma delimited so it can be opened in excel. I can't tell you how many pages long it is because it could give away the number but I will say it is too long to post. We're having a hard time transferring it through google docs.
Shaydo is using Visual Basic in Excel and I think a different method for executing VB. He will need to answer that.

[Captain dungeness]

Contest ending April 25, 2016
Post your calculation or guess by the end of the day on April 25.
You can change your answer up until the end of the 25th.

If you don't know then post a guess, it couldn't hurt.

-Captain D

[Hawk]

My answer is 7

[Juicypotato]

11333

[Haron]

Having solved the first problem (finding the number of legal routes), I've been pondering on the second problem: How to prove that a wrong answer is actually wrong. My preferred choice is to prove, by math, what is correct, but that obviously only works if the target audience understands and accepts the math as correct. I'm willing to give that one more try later (I've found an even easier way to explain it), but I've also been working on other options.

For the other players who have presented their calculations, the natural thing is to point out errors in their calculations. Some have made very elaborate explainations, which is a good thing, because it's easy to point out what is right and what is wrong. That's "good science". For those just presenting a number, I can think of no way to prove that number wrong, except if they present a very small number, in which case one can counter with a list of legal, non-duplicate routes longer than that number.

However, as I understand it, Dungeness is actually compiling a list. Checking if a list is right or wrong IS possible. I've made one program that checks a list for "illegal" routes (fast), and one that checks a list for duplicates (slow). Using this, I've also compiled a list of all legal, non-duplicate trading routes myself. This means that if Dungeness' list is presented in some way (I need to be able to import it, preferably to Excel or MatLab), I DO have a way of proving if that is wrong: If it contains illegal routes or duplicates, I can point out those routes. If it is incomplete, I can check which routes are missing, and present a legal route that is NOT in the list. So, now I'm just waiting for Dungeness' list to be presented in som downloadable format