## Tuesday, September 20, 2011

### Pirates

There's an old type of logic problem which I know by the name of Saints and Pirates.  The central premise is that Pirates always lie and Saints always tell the truth.  Given this, and given a number of statements made by people who are assumed to be either Pirates or Saints, one sets out to determine which ones if any are Pirates.

There are often additional criteria given to assist the solver, and there may be additional information that is to be determined, such as the name of the Pirate, but the overall idea remains the same.

Here is a simple example of such a problem.

There are 4 numbered suspects whose names are Bri, Dee, Cay and Ann, though it is not known which suspect is which.  It is also known that three of the suspects are Saints and that one is a Pirate.  Given the following statements made by suspects 1 and 4, determine the name and suspect number of the Pirate.

Suspect 4: I am not Cay and Bri is not a Saint.
Suspect 1: Either Dee is not a Saint or Cay is not a Pirate.
Suspect 4: Either Suspect 2 is not Bri or I am not a Saint.

Now, feel more than free to solve this and post the answer or, if I've screwed up and allowed for multiple possible answers or no possible answer, feel free to point that out as well.

But the real question is, if you encountered such a problem in an mmo, would you:

1. Look up the answer because you view such problems as annoying obstacles.
2. Look up the answer because you wouldn't want to risk possible negative consequences.
3. Look up the answer only if you couldn't solve it after some time.
4. Avoid looking up the answer even if you were never able to solve it.

I think I'd fall into category 3, though its a moot point since I suspect we are well past the time when developers would bother putting such things into an mmo as they fail to cater to the average player.

Note:  I've made up hundreds of such problems over the years -- so if there were any interest at all, I might post a few more.  Heck, I might post more even if there is no interest.

1. (1) is it for me. I know that I can solve this if I spend some effort. I honestly have no need to prove it. And that's why I don't.

If you want to make me solve this nowadays, you need wrap it up in a way that it seems to be more than just an artificial element to keep my mind busy ;)

2. I hate you John. And I hate riddles, because it seems I still can't help but try to solve them. F*** you! ;)

Anyway ...
Maybe I don't get this the way it is supposed to be solved. I can find at least two solutions.

1-C-Saint
2-A-Saint
3-B-Pirate
4-D-Saint

is a solution. Let's test it:

Suspect 4: I am not Cay and Bri is not a Saint.
Since 4 is a saint this has to be true.
It is.
4 is not C (he is D) and B is the pirate, i.e. not a saint

Suspect 1: Either Dee is not a Saint or Cay is not a Pirate.
Since 1 is a saint this has to be true.
Its is.
Only one of the two must be true and only one is true:
D is actually a saint (false), and C is not the Pirate (true).

Suspect 4: Either Suspect 2 is not Bri or I am not a Saint.
Since 4 is a saint this has to be true.
It is.
Only one of the two must be true and only one is true:
2 is not B, he is A (true). And he (4) is a Saint (false).

---
But the same way you can argue that

1-A-Saint
2-C-Saint
3-B-Pirate
4-D-Saint

is a solution. Since I only switch A and C here, there's no difference in the arguing, both are saints and both are not B which must not be a 2 according to 4.

This just took stole some 30 minutes of life which I could just have well used to tell Syl even more eloquently how wrong she is! ;)

3. The uniqueness of solution is dependent on the question -- in this case the name and suspect number of the Pirate.

While you are correct that the problem does not uniquely determine the names and types of all suspects, it does uniquely determine that suspect 3 is Bri the Pirate.

4. In a way I had, yeah :)

5. @John

lol to be honest, I hope we never get puzzles like these where it matters in an MMO, ha ha ha..!! they make my head hurt and I'm not sure I'm the average player looking for fast reward.
in any case, I like riddles and I would take up the challenge. first thing I'd get myself some paper and I'd spend time figuring it out definitely (albeit I would hate you for it). but then, it is also about 'cost vs. reward' for every individual, so the tolerance decreases if riddling isn't fun to the player (while Nils might get kicks out of it). at some point I would do nr.3 and I suspect most players will - only the point in time may differ greatly.

nr.2 is only really an option for games that know absolute punishment imo. for example in some of the oldschool RPGs it was plain devastating to click one wrong answer, but MMOs aren't exactly constructed that way.

@Nils
You can always try! :P

6. @Syl

Yeah, #2 is representative of the typical old-school rpgs. I hated such things unless I loved the game so much that I didn't mind the thought of playing all the way through over and over and over ....

And yes, MMOs aren't constructed that way at all ... but after a decade of playing them, I'm really tired of the no-consequence advancement treadmill that they've become.

7. I'm not really getting kicks out of it, Syl. In fact, the first thing I did was check whether there was a solution available on the internet. There probably is, but I didn't find one within a minute.

Then I tried a brute force attack. But since I thought the 1-A, 1-B stuff is important, too, there were 96 possibilities which I didn't want to think through.

Then I just started with let's assume 4 is a saint, what follows? and that was actually pretty easy then.

Such riddles in a MMO would not make me have any fun, unless there were solutions on the internet. But of course there are. Anyway, this stuff is just not really immersive. It's too artificial.

8. @Nils

I'd be shocked if there had been a solution on the internet prior to your posting of one. Because the problem was an original that I had made up for the point of this post. :)

I also think your statements of "not really immersive" and "too artificial" are true for you (and the majority of people), but not necessarily everyone. Whether something seems artificial is obviously dependent on the nature of both the player and the virtual world in question. Once the existence of "Saint" and "Pirate" npcs are accepted, it is not that much of a stretch to imagine that the above situation could arise.

Nonetheless, what's true for you is true for you and I'd be foolish to try and argue the point.

For me, I rather enjoy making up such puzzles. I find the challenge of coming up with a minimal set of conditions which uniquely determines the answer to a question an extremely pleasant diversion. On the other hand, I'm not quite as engaged when it comes to solving such problems, especially when posed by other people. ;)

9. Nils is a cheater!!!

=P

10. @Syl: Yeah, but I'm good :)