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The Mark of Intellect Quest

WARNING: This page is full of spoilers.

Contents

  1. Introduction (Minor Spoilers)
  2. Waypoints and Spawns (Minor Spoilers)
  3. The Suspects
  4. The Evidence (Minor Spoilers)
  5. Solution Strategy (Major Spoilers)
  6. Finding the Culprit (Major Spoilers)
  7. Changelog

Introduction (Return to top)

The Mark of Intellect is part of the Mark of the Hero Quest series. More information regarding these quests can be found at swgtest.com or starwarsgalaxies.com. The only prerequisite is the completion of the initial Squill Skull Quest in the Hermit/Squill cave. This quest is itself a prerequisite for receiving the Mark of the Hero badge.

The quest involves finding a Bounty Hunter who tracks down a smuggler on Tatooine, but arrives to find 6 suspects. The BH can't figure out which is the guilty smuggler without help, and that's where you come in.

This seems like an extension to this classic brainteaser: hiking from your home, you come to a fork in the road and see two brothers from town lounging about. Having heard of these brothers before, you know that one always lies while the other always tells the truth. You need to ask which path to take to reach your destination, but how can you find your way without knowing beforehand which person is the liar?

Waypoint and Spawn information (Return to top)

The Quest spawns as a bounty hunter surrounded by his six suspects. All seven are white-name (unattackable) NPCs. They have been seen in the following locations:
Anchorhead (   69 -5381) behind the Cloning Center
Bestine (-1364 -3641) right next to the Starport
Mos Eisley ( 3483 -4644) near the Shuttleport
Mos Entha ( 1544  3123) on the way from Shuttleport A to the Starport
Mos Espa (-2892  2200) in the round enclosed area in the middle of town
Mos Taike ( 3795  2388) near the tavern
Please send a tell or in-game email to Kipper with waypoint information if you see a spawn in Wayfar. The spawns do not appear to follow any pattern. That is, it could spawn in Wayfar, then Anchorhead, then in Wayfar again.

When it spawns, everyone has a single chance to guess the correct smuggler once. As long as people guess incorrectly, the spawn stays and other people are given a chance to guess. Once someone guesses correctly, the spawn disappears after a few seconds and will respawn roughly 20 minutes later. Once it respawns, everyone who hasn't gotten the badge gets another chance to guess, and those who have guessed correctly will no longer be able to participate.

The Suspects (Return to top)

Since the names, clothing, and positioning of the guilty party change each spawn, we can just refer to the smugglers by assigning them numbers. In the end, it is more important to consider what they say, not which number they are assigned, nor what position they are in relative to the BH. The spawn will appear something similar to the following:

1 346
BH
2 5

Here, we arbitrarily number the smugglers from left to right. These short identifiers are easier to work with than full names, etc. Again, the smugglers change position every time, so if 2 thinks 3 or 5 is guilty, that may change to 4 accusing 1 or 3 for the next spawn.

The Evidence (Return to top)

Now that we've identified the smugglers, we have take a look at what they have to say. You're given the options of asking them about the allegedly smuggled item and asking them about the other smugglers. It appears that asking about the item is useless. When asked about the other smugglers, each smuggler might say different things but they will be stating the same information, merely with different words. For my spawn, the statements were as follows:
  1. 3 AND (2 XOR 4) lie
  2. 2 AND 6 are innocent
  3. 2 AND 4 lie
  4. 2 OR 3 are guilty
  5. two of the other smugglers are liars, but three are truthful
  6. 1 lies
Additionally, the bounty hunter says that the smuggler captain happens to be trustworthy. For this particular spawn, the captain was number 5, and we'll refer to him as 5 from now on. Note: XOR means either one can be true, but not both.

Solution Strategy (Return to top)

To begin, we can draw truth tables to represent each suspect's testimony.

Suspects 2 and 3
 bitwise AND      
--------------
A B A&B !(A&B)
- - --- ------
0 0  0    1   
0 1  0    1   
1 0  0    1   
1 1  1    0   
--------------
Suspect 4
  bitwise OR
--------------    
A B A|B !(A|B)
- - --- ------
0 0  0    1
0 1  1    0
1 0  1    0
1 1  1    0
--------------
Suspect 1
      AND with XOR
------------------------
A B C A&(B+C) ![A&(B+C)]
- - - ------- ----------
0 0 0    0         1
0 0 1    0         1
0 1 0    0         1
0 1 1    0         1
1 0 0    0         1
1 0 1    1         0
1 1 0    1         0
1 1 1    0         1
------------------------
How to read truth tables: If we think a particular testimony is true, we look to the second to last column of the corresponding table and see which rows are marked with 1s. Those rows represent possibilities that need to be examined. If we think that a particular testimony is false, we would look for 1s in the last column. For example if 3 is lying, we look at the fourth column of 3's table and see three marked rows. The table tells us that either both 2 and 4 are telling the truth, or one of them is lying. We would then consider the ramifications of each of these three cases.

       Example: Suspect 3        
---------------------------------
   2        4        3       3   
-------  -------  -------  ------
2 truth  4 truth           3 lies
2 truth  4 lies            3 lies
2 lies   4 truth           3 lies
2 lies   4 lies   3 truth        
---------------------------------

Assumption A: If someone is telling the truth, his entire statement is assumed to be true and we can consider the second to last column in the appropriate truth table. If someone is lying, we assume his entire statement is false. This is the same as negating the entire statement and using the rightmost column in the truth table.

Assumption B: There is exactly one guilty party. Any situation where no one ends up guilty or any situation that implicates more than one person will be discarded.

Convention: Numerals like 2 and 5 will refer to suspect identifiers, and all other instances of numerical values will be spelled out. Masculine pronouns will be used for brevity even though not all the smugglers are necessarily male.

Strategy: We begin by assuming that one suspect is either honest or lying, and see what conclusions can be drawn. We will discard the cases that lead to contradictions, ignore the cases that lead to ambiguity, and look for the solution in the remaining possibilities.

Finding the Culprit (Return to top)

First assume that 6 is lying. This implies that 1 is telling the truth. We look at the third column in the truth table for 1 and see that this is only possible in rows six and seven. These two rows imply that 3 is lying, which in turn implies that at least one of 2 and 4 are telling the truth. This is true, as either 2 or 4 has a zero in rows six and seven.

In row six, 2 is telling the truth and 4 is lying. 2's testimony states that 2 and 6 are innocent, and if 4 is lying, his testimony implies that neither 2 or 3 is guilty. We end up with zero guilty parties and discard this possibility.

In row seven, 2 is lying and 4 is telling the truth. That means one of 2 or 6 is guilty, but 4 lets us know that one of 2 or 3 is guilty. The intersection implicates suspect 2.

Now assume that 6 is honest. This implies that 1 is lying, so we can look at the fourth column of the truth table for suspect 1. There are six situations that make this possible. Let's see what happens if 3 is telling the truth (first four rows). If 3 is telling the truth, then 2 and 4 are both lying, so no zeros can appear. We can discard rows one, two, and three. Consider row four, which tells us 2 and 4 both lie. Thus we know that 2 or 6 is guilty, but 4 tells us neither 2 nor 3 is guilty, implicating suspect 6.

Consider row eight. 3 is lying, which means both are telling the truth, contradicting the rest of the row, so we discard 8.

Consider row 5. 3 is lying, which means both are telling the truth. The intersection of 2 and 4's testimony implicates suspect 3.

Let's revisit the testimony of 5. We are told by the bounty hunter that we can trust what he says, so there are three truthful people among the other five. There is only a single scenario above where a single person is implicated and three people are telling the truth. Namely, 3 is implicated when 6, 4, and 2 are telling the truth.

Note that the culprit won't always be in position 3, but the guilty smuggler will always say the same thing, namely that two others are liars.

Changelog (Return to top)

 06/27/04 
Updated with the fact that the smuggler captain can be trusted. This leads to the same conclusion as before, but now we can be more confident in our answer.

 06/23/04 
Second version of analysis, with help from rec.puzzles and Utess

 06/18/04 
First version made public
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