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Tedv's Logic Puzzle

From YPPedia

Tedv's Logic Puzzle of May 2004 was a familiar event that took place both on the forums in in the game itself. Players were given the task of finding clues scattered about the game in the news section of public, Ringer-owned buildings. They then had to solve the puzzle presented by the clues, and e-mail the solution, and a proof of the solution, to Tedv.

Contents

The Prizes

For presenting both the fastest and the most elegant solution, Sparrowhawk walked away with a blue/red parrot. The following players also took away prizes based on their performance:

  • Runner Up: AquaDrake - Custom Sloop and Tricorne
  • 3rd: Adain - 10k and Tricorne
  • 4th: Sloshy - Tricorne
  • 5th: Umbergryphon - Tricorne
  • 6th: Robertdonald - Tricorne
  • 7th: shockedfrog - Tricorne

The Clues

A) Alpha Bank:
Chris says, "The worst sword fighter and Tim are two of the biggest liars I've ever met."

B) Epsilon Notice Board:
Chris says, "Last night when I was drinking rum with the Sailmaster, the best sword fighter, and the average sword fighter, the Sailmaster whined that his sword skill was the worst of the four of us."

C) Epsilon Tailor Bazaar:
Tim says, "I just heard the best sword fighter mock Eric, saying Eric's sword skills were even worse than mine."

D) Alpha Weaver Bazaar:
Chris says, "I heard Tim say that the second best sword fighter is a liar."

E) Epsilon Palace Entrance:
Tim says, "I'd bet my one good eye that Paul hasn't told the truth once in his life."

F) Guava Market:
Paul says, "Ben lies more than the devil himself."

G) Gaea Market:
Ben says, "I wouldn't trust the average sword fighter to tell the truth if his life depended on it."

H) Papaya Market:
Eric says, "Either the Quartermaster and Navigator are both worse than the average sword fighter or both better than him."

I) Gaea Realtor:
Ben says, "Either the Surgeon is a worse fighter than the Midshipman or the Quartermaster is the best sword fighter."

The Solution

There are several possible proofs for the solution to this puzzle. One such proof, provided by Tedv, is shown below.

SOLUTION:

Mutineers:
Sailmaster Tim (2nd Worst)
Quartermaster Christ (2nd Best)
Navigator Ben (Best)

Innocent:
Midshipman Eric (Worst)
Surgeon Paul (Average)


PROOF:

Start by assigning each sword fighting rank a number from 1 (best) to 5 (worst).

By clue C, Tim is not 1 (best). Tim is also not swordsman 5 (worst) by clue A (and neither is Chris, since Chris can't have met himself.) Clue D implies Tim isn't 2 (second best). So Tim must be 3 or 4.

Since Tim calls Paul a liar in clue E, and Paul calls Ben a liar in clue F, Tim and Ben have the same truth state, which is the opposite of Paul's. And since Ben calls the average swordsman a liar, that swordsman has the opposite truthstate as Tim and Ben (and the same as Paul). So in particular, Tim can't be the average swordsman. Therefore Tim is swordsman 4, the second worst swordsman. (+1 = 1 point)

By the information in clue B, Chris is definitely not swordsman 1 or 3. Clue A proved Chris couldn't be 5, so Chris is either swordsman 2 (second best) or 4 (second worst). Since Tim is swordsman 4, Chris must be 2, the second best swordsman (+1 = 2 points).

In clue D, Chris says, "I heard Tim say that the second best sword fighter is a liar." But Chris is the second best sword fighter, so Chris is really saying, "Tim said Chris is a liar". If Chris is telling the truth, Tim must be a liar for calling Chris a liar. And if Chris is lieing, then Tim actually claimed "Chris tells the truth", which is also a lie. So whether or not Chris tells the truth, Tim must be a liar (+1 = 3 points).

In clue E, Tim calls Paul a liar, so Paul must tell the truth (+1 = 4 points). And in clue F, Paul calls Ben a liar, so Ben must lie (+1 = 5 points).

Reviewing clue B, the one about the sailmaster, Chris claims that the Sailmaster claims he is a worse fighter than 1, Chris, and 3. Since Chris is 2, the Sailmaster must be either 4 (Tim) or 5 (currently unknown). If Chris is telling the truth, then the Sailmaster is also telling the truth. If Chris is a liar, than the Sailmaster actually claimed, "I am a better sword fighter than at least one of 1, 2, or 3". This is clearly a lie. So the Sailmaster and Chris have the same truth telling state.

Now look at clue A. Chris claims that both the worst sword fighter (5) and Tim are liars. Well Tim is definitely a liar, so Chris is telling the truth if 5 is a liar. But if 5 actually tells the truth, then Chris is a liar. This means Chris and swordsman 5 have opposite truth telling states

Therefore the Sailmaster can't be 5, the worst sword fighter. This means the Sailmaster is the second worst fighter, Tim (+1 = 6 points). Since Tim, the Sailmaster, is a liar, Chris must also be a liar (+1 = 7 points). And the worst sword fighter must tell the truth.

To recap:
Chris: (L) #2
Tim: (L) #4 Sailmaster
Ben: (L) ??
Paul: (T) ??
Eric: (?) ??

Since the worst sword fighter tells the truth and Ben lies, Ben can't be the worst sword fighter. And Ben also calls the average swordsman a liar in clue G, so that pirate isn't Ben either. Pirates 2 and 4 are Chris and Tim respectively, so Ben must be the best sword fighter, #1 (+1 = 8 points).

This leaves Paul and Eric as the average (#3) and worst (#5) fighters. According to clue C, Tim claims that Ben said Eric was a worse fighter than Tim. Tim is a liar though, so Ben actually said that Eric was better than Tim. And since Ben is a liar as well, the truth is that Eric is indeed worse than Tim. Tim is the second worst sword fighter, so Eric must be the worst (+1 = 9 points). This leaves Paul as the average sword fighter (+1 = 10 points). Since the worst sword fighter tells the truth, Eric must tell the truth (+1 = 11 points).

Recap:
Ben: (L) #1
Chris: (L) #2
Paul: (T) #3
Tim: (L) #4 Sailmaster
Eric: (T) #5

Clue H, spoken by Eric, must be a truthful statement. Either the Quartermaster and Navigator are both worse than 3 or both better than him. Well neither of them can be swordsman 3, and they can't both be worse (since the Sailmaster is swordsman 4), so they must both be better.

Clue I is a lie because it was spoken by Ben. Ben claimed that, "Either the Surgeon is a worse fighter than the Midshipman or the Quartermaster is the best sword fighter." Since this is an OR statement that is false, both halves must be false. So the Surgeon is NOT worse than the Midshipman and the Quartermaster is NOT the best sword fighter. It was previously proved that the Quartermaster must be either 1 or 2, and the Quartermaster can't be 1 anymore. So the Quarter master must be #2, the second best fighter, who is Chris. According to Eric's previous clue, this leaves the best sword fighter, Ben as the Navigator (+2 = 13 points).

The only two unassigned ranks Midshipman and the Surgeon, for Eric and Paul. Since the Surgeon is a better fighter than than the Midshipman, and Paul is better than Eric, Paul is the Surgeon and Eric is the Midshipman (+2 = 15 points).

Ben: (L) #1 Navigator
Chris: (L) #2 Quartermaster
Paul: (T) #3 Surgeon
Tim: (L) #4 Sailmaster
Eric (T) #5 Midshipman

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