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Why You Should Have Picked Rutu


by max02468

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Please note: Percent calculations in this article were rounded at the author's discretion in order to keep things clean. Within the context of the article there really isn't a difference between something having a probability of 8.325% or 8.5%. Thank you.

This year's Festival of Neggs took a surprising turn of events when, just over a week ago, the Negg Faerie's Assistant, Zaira, accidentally uncovered a long forgotten mystery during some routine spring cleaning. (Don't you just hate it when that happens?) Behind a dusty old cabinet was a journal, written by someone guarding a fantastic secret. The author of the journal was in possession of an incredibly powerful Negg; the clockwork Negg as it was called. To keep it out of the reach of those with dubious intentions, the author formed a team to conceal the location of the Negg. Five members of the team were to take five different Neggs to five different locations and hide them in secret.

However, Zaira soon noticed that the entries in the journal seemed to contain cryptic clues about where each member of the team took their assigned Negg. And so at Zaira's request, the members of the Neopian community assembled to tackle this great mystery and uncover the location of the infamous clockwork Negg (with the purist of intentions, I'm sure). Day by day, Zaira presented us with entries from the journal and asked us to answer the questions, which team member was assigned to transport the clockwork Negg and what is the location of its hiding place? What I intend to show here is that for every day we were allowed to submit our guesses, one combination of name and location always had the highest probability of being the correct answer to the previously stated questions.

While spread over the duration of several days, as a whole, the puzzle contained in the journal was a type of logic problem. Given a series of simple statements of fact, you were required to use deductive reasoning to determine which Negg each member of the team was carrying, and where they were taking that particular Negg. Deductive reasoning is fairly straight-forward and actually a discipline of mathematics. (That's right. You were tricked into doing math.) The key was to break down sentences in the journal to simple statements of the form,

[Name/Title] was (not) transporting the [Negg]

[Name/Title] was (not) going to [Location]

The [Negg] was (not) going to [Location]

[Name] was (not) the [Title]

And combine them to eventually make a final conclusion of the form,

[Name] is transporting the [clockwork Negg] to [Location].

Here's a simple hypothetical example:

[Rutu] was going to [Brightvale]

The [clockwork Negg] was going to [Brightvale]

Therefore,

[Rutu] was transporting the [clockwork Negg] to [Brightvale]

While the entries in the journal were not always so straight-forward, they could always be broken down into these simple statements of fact. And it was important that only these factual statements were used to determine the correct answer to the logic puzzle. As soon as anyone began to make assumptions about the team members' titles based on their clothing or trying to match the Neggs' supposed physical properties to the theme of the hiding locations, they began to deviate from the path of deductive reasoning and into a dark abyss of speculation and misinformation. Do not go there; for that way lies madness.

Now the [Name]s of the five members of the team were Rutu, Selvin, Voughn, Hurok, and Ricky.

The five types of [Negg] were sand, glass, plant, cloud, and clockwork.

The five [Location]s were Lost Desert, Altador, Shenkuu, Kiko Lake, and Brightvale.

And the five [Title]s given to members of the team were explorer, blacksmith, wizard, knight, and botanist.

Entry 2, 5 and 8

On the first day Neopians were allowed to submit their guesses, April 13th, journal entries 2, 5 and 8 were available to the community. From the clues given in these entries, it was possible to deduce that only 9 combinations of name and location were possible answers to the question, "Who was transporting the clockwork Negg, and where were they going with it?"

What we knew (the number in brackets refers to which journal entry the information can be found):

- Rutu was going to Shenkuu (5)

- Selvin was not going to Lost Desert (2) or Brightvale (8)

- Voughn was transporting the cloud Negg (5)

- The glass Negg was going to Brightvale (8)

That left us with the following [Name]; [Location] pairings for the clockwork Negg:

- Rutu; Shenkuu

- Selvin; Kiko Lake, or Altador

- Hurok; Lost Desert, Kiko Lake, or Altador

- Ricky; Lost Desert, Kiko Lake, or Altador

Now with 9 possible [Name]; [Location] combinations, it might have been tempting to assume that, all things being equal, each combination had the same probability of being the correct answer to the question, who took the clockwork Negg where? I have to admit; I too initially thought this to be the case and broke down the probability of each one rather naively:

Rutu; Shenkuu = 11%

Selvin; Kiko Lake = 11%

Selvin; Altador = 11%

Hurok; Lost Desert = 11%

Hurok; Kiko Lake = 11%

Hurok; Altador = 11%

Ricky; Lost Desert = 11%

Ricky; Kiko Lake = 11%

Ricky; Altador = 11%

Hubrid Nox's ghost stole the Negg and it using it to plot Neopia's destruction = 1%

But looking at this breakdown closely you should notice something is a little off (okay, maybe two things). Why would Hurok and Ricky have a 33% chance of holding the clockwork Negg, while Rutu only had an 11% chance? Just because they had more location options available to them did not make it more likely that they were the ones meant to be transporting the clockwork Negg on their journeys. Given the nature of the mystery (ie. a deductive logic puzzle), there should be no correlation between how many places one member could visit and the probability that they were transporting the clockwork Negg. These factors should have been considered independent of each other from a probability standpoint. In fact, from a completely objective perspective (ie. all things really being equal), given 4 members to choose from, each actually had a 25% chance of being the correct answer to the question, "Who was transporting the clockwork Negg?"

The next question was then obviously, "If [Name] was transporting the clockwork Negg, where were they going with it?" This was where Rutu shone. Because it was explicitly stated that Rutu was "to be going" to Shenkuu in entry 8, Shenkuu is the only possible location choice for Rutu. There was a 100% chance that, if Rutu was transporting the clockwork Negg, it was going to Shenkuu. On the other hand, if Selvin was transporting the clockwork Negg, there was then a 50% chance that it would be going to Kiko Lake and a 50% chance that it would be going to Altador. If either Hurok or Ricky were the ones to have transported the clockwork Negg, then each of their three possible hiding locations, Lost Desert, Kiko Lake or Altador, would only have had an ~33% chance being correct.

So what does this mean? This means that, at this point in the puzzle, each combination of Hurok and Lost Desert, Kiko Lake and Altador only had an 8.5% of being the correct answer to the question, "Who was transporting the clockwork Negg and where were they going with it?" The math was fairly simple. You take the probability that Hurok is transporting the clockwork Negg (25%) and for each possible hiding location multiply by the probability that they were going there, like so:

Hurok (25%) x Lost Desert (33%) = 8.5%

Hurok (25%) x Kiko Lake (33%) = 8.5%

Hurok (25%) x Altador (33%) = 8.5%

The same conclusion was reached for Ricky and each of their 3 possible destinations. Selvin fared slightly better. If Selvin happened to be the one transporting the clockwork Negg, each of their possible destinations had a 50% chance of being the correct hiding location.

Selvin (25%) x Kiko Lake (50%) = 12.5%

Selvin (25%) x Altador (50%) = 12.5%

However, as I mentioned before, there was only one possible hiding location for Rutu. This meant that if Rutu was transporting the clockwork Negg there was a 100% chance that they were going to Shenkuu. Meaning that the [Name]; [Location] combination of Rutu and Shenkuu, actually had a 25% chance of being the correct answer. That's 2 or 3 times more likely than any other possible combination!

The same results could be achieved by determining the probability that each location had for being the correct destination for the clockwork Negg and then multiplying by the percent probability that each character had of being the correct member to travel there. Since there's much more to cover, this will be left as an exercise for the reader.

Entry 9

The ninth journal entry cut down the possible number of correct solutions even further, when it was stated that Hurok was excused from carrying the clockwork Negg. Much to the dismay of Hurok supporters, this left us with only 6 possible combinations of [Name]; [Location] pairings for the clockwork Negg.

- Rutu; Shenkuu

- Selvin; Kiko Lake, or Altador

- Ricky; Lost Desert, Kiko Lake, or Altador

With only three possible choices for the transporter of the clockwork Negg, each member had a ~33% probability of being the correct one. After completing the math, we'll see that once again the combination of Rutu and Shenkuu came out as the answer most likely to be correct at the time:

Rutu (33%) x Shenkuu (100%) = 33%

Selvin (33%) x Kiko Lake(50%) = 16.5%

Selvin (33%) x Altador (50%) = 16.5%

Ricky (33%) x Lost Desert(33%) = 11%

Ricky (33%) x Kiko Lake(33%) = 11%

Ricky (33%) x Altador (33%) = 11%

Entry 12

The twelfth journal entry was met with yet another batch of cries, as supporters of Ricky were forced to re-submit their guesses, when the information given in the journal ruled out the possibility of them being the clockwork Negg's transporter. With Ricky out of the running, the number of possible correct combinations was cut in half to a partly 3.

What we knew by this point:

- Voughn was transporting the cloud Negg (5)

- The glass Negg was going to Brightvale (8)

- The blacksmith was transporting the sand Negg (12)

- Rutu was not the blacksmith (12)

- Selvin was the wizard (2)

- Rutu was going to Shenkuu (5)

- Selvin was not going to Lost Desert (2) or Brightvale (8)

With this information and by process of elimination, the only Neggs that Rutu and Selvin could possibly carry were either the clockwork Negg or the yet unnamed plant Negg, leaving us with the only remaining possible answers:

Rutu(50%) x Shenkuu (100%) = 50%

Selvin (50%) x Kiko Lake(50%) = 25%

Selvin (50%) x Altador (50%) = 25%

Again from a statistical perspective, the [Name]; [Location] combination of Rutu; Shenkuu remained the most likely correct answer. Even though both Rutu and Selvin had a 50% chance of being the one to transport the clockwork Negg, it was also necessary to take into consideration the 50/50 probability in choosing between either Kiko Lake or Altador as Selvin's destination in order to determine the probability of either of those combinations being correct.

Entry 14

The fourteenth journal entry provided the proverbial "straw that broke the camel's back" for Selvin supporters. And boy was it a whopper. Here it was proclaimed (high and low throughout the land) that the plant Negg was destined for Kiko Lake. Since we knew Shenkuu was the only possible destination for Rutu, the only member available to take the plant Negg was Selvin.

All hail the great botanist, Rutu!

As you can see, throughout the entire puzzle, Rutu transporting the clockwork Negg to Shenkuu was actually the [Name]; [Location] combination with the highest probability of being correct. While this article does have the benefit of hindsight, and the correct answer could very well have been something as unlikely as Hubrid Nox stealing the clockwork Negg and using it to wreak a terrible vengeance on us all (he totally would if he could), it's important to know how to approach a logic puzzle from an objective perspective and not get bogged down by frilly language and conspiracy theories. No matter how "logical" a theory may sound, as soon as they start using words along the lines of "I think this implies that…" you better run for the hills, because what's to follow is stream of debating posts consisting of round about logic and mental gymnastics that would put any professional yooyuball player to shame. And maybe even a flame war or two.

What I hoped to illustrate in this article was that despite the fact that the initial rounds of submitting an answer were based on very limited information, and was essentially guesswork, it does not mean that a logical and objective approach to the problem is impossible to come by. Even a smart gambler should know how to work the odds into his or her favour. Now if you'll excuse me, I have to go find today's zig-zag Negg. You have been keeping up the festival, haven't you?

 
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