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darkSpyro - Spyro and Skylanders Forum > Stuff and Nonsense > I've got a problem for you to solve, darkSpyro.
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I've got a problem for you to solve, darkSpyro. [CLOSED]
Samius Hunter Gems: 9573
#1 Posted: 09:01:15 11/01/2016 | Topic Creator
So, here's a little something for you to think about. Put your answers in spoilers so that others don't accidentally see them.
Also try to explain how you came to that exact conclusion. If you simply guessed correctly, I won't let you know if you were right or not.
You can use a pen and paper to solve the problem, as it might be a bit difficult to do so in your head.

I got the idea in math class and made up all the names of the characters and locations, So you shouldn't be able to find the right answer online by using Google, etc.

---

Gentleman detective Radford was visiting Baron Battenberg's estate, where a peculiar problem needed to be solved. While the Baron had been away, one of his servants had walked across the white rug in his living room wearing muddy shoes. From the footprints it was obvious that there was only one culprit.
Detective Radford had three suspects: Alfred, Beatrice and Casper. He was absolutely sure that one of the three was guilty.

Radford interrogates the suspects. Here is what they had to say:

Alfred: "Casper is surely innocent."

Beatrice: "Alfred is innocent, and I am too."

Casper: "Either Alfred is innocent or I am guilty. Both may also be true."

Considering the fact that the servants of the Battenberg estate were known to be dishonest, and only those of them who were innocent spoke the truth, Detective Radford was able to quickly deduce the identity of the culprit.

Who was guilty?

To clarify: In the Battenberg estate those who are innocent always speak the truth, and those who are guilty always lie.

Also removed some typos.
Edited 4 times - Last edited at 17:55:22 11/01/2016 by Samius
Dark Snap Shot Gold Sparx Gems: 2648
#2 Posted: 13:07:23 11/01/2016
I think its
casper
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Psn-Zydren8cookie, FC 3024-5345-8692
Greeble Emerald Sparx Gems: 4431
#3 Posted: 13:09:55 11/01/2016
I'm going with
Casper


Just because that's how i roll.
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^ You all know it's true
Windumup Emerald Sparx Gems: 3217
#4 Posted: 14:27:59 11/01/2016
It's obviously
Beatrice
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Ugh I wish my body wasn't a mess
mega spyro Emerald Sparx Gems: 3993
#5 Posted: 14:29:12 11/01/2016
I know the correct answer:


42
---
Dead
thumper Ripto Gems: 3519
#6 Posted: 14:46:11 11/01/2016
Only a guess, but it's probably wrong?

Alfred said Casper was innocent. Beatrice said Alfred is innocent. Ruling Alfred and Casper out, it had to be Beatrice?
arceustheprime Ripto Gems: 5362
#7 Posted: 15:24:17 11/01/2016
alfred cause two people said he was innocent and bros before baron battenberg

ytrtujiyttyg
I-Brawler Emerald Sparx Gems: 3565
#8 Posted: 15:29:18 11/01/2016
Quote: thumper
Only a guess, but it's probably wrong?

Alfred said Casper was innocent. Beatrice said Alfred is innocent. Ruling Alfred and Casper out, it had to be Beatrice?


Going this for the exact same reasoning.
---
you never saw me
sonicbrawler182 Platinum Sparx Gems: 7105
#9 Posted: 16:24:53 11/01/2016
Figured it out in my head mostly, but sort of made realisations that changed things while typing my explanation. I'm fairly sure of my final deduction:


Alfred is guilty.

I personally find these kind of puzzles fairly simple to solve.

Basically, I read through all of the statements three times, each time assuming a different one of the three is guilty. If there is one person's statement that is consistently causing a contradiction in each scenario, that person is likely the real culprit.

In this case, the statement that doesn't fit and consistently creates a contradiction, no matter who you assume isn't telling the truth, is Casper's.

If you assume Alfred is guilty, then Alfred's claim that Casper is innocent contradicts Casper's claim that Alfred is innocent and that Casper is guilty, as well as Beatrice's claim that Alfred is innocent.
If you assume Beatrice is guilty, it contradicts her claim that she is innocent.
If you assume Casper is guilty, then...Casper's claim is actually completely true, in all three thirds. But it causes Alfred's statement to be untrue.

OK, so by going through each statement three times, each time assuming a different culprit, we still don't have a definite answer as to who the culprit is. So what do we do now?

Well, this is where a particular part of the puzzle's description comes into play:

Quote:
Considering the fact that the servants of the Battenberg estate were known to be dishonest, and only those of them who were innocent always spoke the truth, Detective Radford was able to quickly deduce the identity of the culprit.


It states that "the residents are known to be dishonest", so that means everyone is saying something untrue. But it also says "only those of them who were innocent always spoke the truth". So let's look at things from that angle.

We've already gone through the contradictions, and Casper is the one who always creates a contradiction every time (while the others bare contradictions, it's Casper's three way statement that always causes them), but I opened saying that Alfred is guilty. Where did I get that from?

The fact is that, there is no scenario where two people are completely truthful, and one is left the sole liar. So if we count up how many times each person tells the truth in each possible scenario, we might notice something. 1 point represents partial truth, 2 points represent a full truth:

Truth Count
If Alfred is guilty
Alfred: 2
Beatrice: 1
Casper: 1

If Beatrice is guilty
Alfred: 2
Beatrice: 1
Casper: 2

If Casper is guilty
Alfred: 0
Beatrice: 2
Casper: 2

As you can see from the above count, the only assumed scenario where someone has a statement that is completely dishonest and not just partially dishonest, is the one where we assume Casper is guilty. And the dishonest person there is Alfred.

Therefore, he is the only possible culprit, according to the part of the puzzle I quoted. Beatrice and Casper "always spoke the truth", to some degree, even if not completely, in each scenario. While this new found conclusion that Alfred is the culprit forces Casper into a position where he is partially dishonest, the criteria of the puzzle never states that the innocent can't be dishonest - merely that they were known to be dishonest and that their statements always contain the truth if they are innocent, even if it's only some of it. Alfred is the only one who can be in a situation where he doesn't even do that much, even if you have to assume Casper as the culprit to reach that conclusion.
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"My memories will be part of the sky."
Edited 5 times - Last edited at 16:34:03 11/01/2016 by sonicbrawler182
Greeble Emerald Sparx Gems: 4431
#10 Posted: 16:30:36 11/01/2016
Quote: sonicbrawler182
Figured it out in my head mostly, but sort of made realisations that changed things while typing my explanation. I'm fairly sure of my final deduction:


Alfred is guilty.

I personally find these kind of puzzles fairly simple to solve.

Basically, I read through all of the statements three times, each time assuming a different one of the three is guilty. If there is one person's statement that is consistently causing a contradiction in each scenario, that person is likely the real culprit.

In this case, the statement that doesn't fit and consistently creates a contradiction, no matter who you assume isn't telling the truth, is Casper's.

If you assume Alfred is guilty, then Alfred's claim that Casper is innocent contradicts Casper's claim that Alfred is innocent and that Casper is guilty, as well as Beatrice's claim that Alfred is innocent.
If you assume Beatrice is guilty, it contradicts her claim that she is innocent.
If you assume Casper is guilty, then...Casper's claim is actually completely true, in all three thirds. But it causes Alfred's statement to be untrue.

OK, so by going through each statement three times, each time assuming a different culprit, we still don't have a definite answer as to who the culprit is. So what do we do now?

Well, this is where a particular part of the puzzle's description comes into play:

Quote:
Considering the fact that the servants of the Battenberg estate were known to be dishonest, and only those of them who were innocent always spoke the truth, Detective Radford was able to quickly deduce the identity of the culprit.


It states that "the residents are known to be dishonest", so that means everyone is saying something untrue. But it also says "only those of them who were innocent always spoke the truth". So let's look at things from that angle.

We've already gone through the contradictions, and Casper is the one who always creates a contradiction every time (while the others bare contradictions, it's Casper's three way statement that always causes them), but I opened saying that Alfred is guilty. Where did I get that from?

The fact is that, there is no scenario where two people are completely truthful, and one is left the sole liar. So if we count up how many times each person tells the truth in each possible scenario, we might notice something. 1 point represents partial truth, 2 points represent a full truth:

Truth Count
If Alfred is guilty
Alfred: 2
Beatrice: 1
Casper: 1

If Beatrice is guilty
Alfred: 2
Beatrice: 1
Casper: 2

If Casper is guilty
Alfred: 0
Beatrice: 2
Casper: 2

As you can see from the above count, the only assumed scenario where someone has a statement that is completely dishonest and not just partially dishonest, is the one where we assume Casper is guilty. And the dishonest person there is Alfred.

Therefore, he is the only possible culprit, according to the part of the puzzle I quoted. Beatrice and Casper "always spoke the truth", to some degree, even if not completely, in each scenario. While this new found conclusion that Alfred is the culprit forces Casper into a position where he is partially dishonest, the criteria of the puzzle never states that the innocent can't be dishonest - merely that their statements always contain the truth, even if it's only some of it. Alfred is the only one who can be in a situation where he doesn't even do that much, even if you have to assume Casper as the culprit to reach that conclusion.


I just read that and a part of my brain just exploded from all the logic.
---
^ You all know it's true
Samius Hunter Gems: 9573
#11 Posted: 16:52:26 11/01/2016 | Topic Creator
I suppose I should remove the word "always" from "always spoke the truth", since it may lead some people to think that sometimes those who are guilty may also speak the truth, which is not the case.

So to clarify: In the Battenberg estate those who are innocent always speak the truth, and those who are guilty always lie.

I'll also edit this into the first post.
CAV Platinum Sparx Gems: 6430
#12 Posted: 17:30:14 11/01/2016
[User Posted Image]-----

Alfred speaks of the innocence or guilt of another man, Casper. By the logic dictated in your puzzle, he would only lie if he were guilty. Why would he throw himself under the bus to protect Casper?

Beatrice claims Alfred is also innocent, and that she herself is as well. If they were to lie then that would mean both are guilty, which cannot be possible since it's evident that only one set of footprints has gone onto the carpet.

And Casper claims that either Alfred is innocent or he is guilty. Once again we have someone speaking for Alfred's behalf, but this time with the twist that he presents the possibility that he's guilty of the crime himself. Problem is that being guilty would require him to tell a lie and we once again fall into the spot where that would mean both of them are guilty or that Alfred is guilty over Casper. Try to follow the concept of both statements being true and then we run into a bit of a paradox where the self proclaimed guilty party could be telling the truth when the guilty party will always tell a lie. Unless you want to get selective in which parts of Casper's statements are a lie, in which case it's not exactly "always" lying now is it?

The thing is that while the servants are known to be dishonest, who said Battenberg could not be dishonest?

Alfred could be a possibility, but I'm somewhat leaning towards Battenberg. Perhaps in a bid to pin the blame on one of the servants he stepped out with the rug and dirtied it up with muddy shoes (the puzzle doesn't mention any mud being found anywhere else on the floor or in the house, and the use of the word rug suggests that it only covers a portion of the room rather than the entire floor like a carpet would).

And with your new statement of "those in the Battenberg estate innocent always speak the truth and those guilty always lie" you become more broad and open up the possibility of those in the estate outside of servants. Ergo you can reason that Battenberg is just as guilty of this behavior as those servants and that he's the one that has been lying the whole time about either the servants muddying up the rug while he was away or, hell, even the possibility that he was ever away to begin with (why would the detective believe the servants when they say Battenberg was always home when they're claimed to be notorious liars?).

My guess is that it's Baron Battenberg himself.
StriderSwag Gold Sparx Gems: 2769
#13 Posted: 17:35:41 11/01/2016
samius it's 10:30 AM it's too early for this ****
Samius Hunter Gems: 9573
#14 Posted: 17:56:14 11/01/2016 | Topic Creator
Quote: StriderSwag
samius it's 10:30 AM it's too early for this ****


It's almost 20:00 here.
StriderSwag Gold Sparx Gems: 2769
#15 Posted: 18:05:25 11/01/2016
Quote: Samius
Quote: StriderSwag
samius it's 10:30 AM it's too early for this ****


It's almost 20:00 here.



ITS 10 HERE U NEED TO STOP WITH THE PUZZLE
Samius Hunter Gems: 9573
#16 Posted: 18:18:49 11/01/2016 | Topic Creator
Quote: StriderSwag
ITS 10 HERE U NEED TO STOP WITH THE PUZZLE


Nothing starts the day like a good puzzle!

But yeah, alright, I suppose I should reveal the correct answer now. In the end this got a lot more replies than I thought it would. Instead of quoting everyone I'll post the correct answer here in spoilers, along with the explanation.

If you haven't yet figured the problem out yourself and want to do so, don't open this spoiler. Just a while ago I added a clarification to the first post that might help you if you tried it before and were having trouble.

Casper stated that either Alfred is innocent or he himself is guilty (or both). He must be speaking the truth, since his statement left open the possibility of himself being guilty. Had he been the culprit, he would've been both guilty and honest, which is not possible in the Battenberg estate.

Since Casper can not be guilty, what he said about Alfred being innocent must be true. Therefore we are left with only a single option: Beatrice must be the culprit.

What makes this problem seemingly difficult to solve, is the fact that Beatrice also stated that Alfred was innocent. Given that Beatrice was guilty, she must have been lying about that also (as those who are guilty always lie in the Battenberg estate), thus leading us into what appears to be an impasse.

But here's the thing; because of the conjunction "and", only one of the things that Beatrice implied must be untrue for her statement to also be untrue. This means that she was still lying even though Alfred was innocent.
So while the statement "Alfred is innocent" is true, Beatrice's statement "Alfred is innocent, and I am too" is a lie.
By their nature statements can only be either true or untrue. "Half truths" are deceptive statements, and though they may contain some truth, that does not make the statements themselves true.

---
In a way Crookshanks got it right. Since nobody other than herself specifically stated that Beatrice was innocent, but did so for the other two suspects, the only way for there to be only one liar and culprit was for it to be Beatrice.

Thumper was close with her explanation too. It was not quite there but her answer was correct.

Arceustheprime gets an A+ for effort, but her answer was not correct.

As far as I can tell sonicbrawler182 got a bit confused with how I worded the description at first. Also, Beatrice's statement wouldn't have been contradicted by her being guilty, because she would've been lying if that was the case.

It looks like CAV fell into the trap laid by the all-mighty "and".
---

(From hereon I'm just rambling a bit about math, just ignore it if you're not interested.)

I mentioned that I came up with this problem in math class. We're currently going through sentential logic, and it's a fairly simple problem to solve if you take all the statements given by the suspects and formalize them by boiling them down into three premises: A, B and C.

A = Alfred is innocent.
B = Beatrice is innocent.
C = Casper is innocent.

Alfred states: C (Casper is innocent)

Beatrice states: A^B (Alfred is innocent and Beatrice is innocent (both must be true for the statement to be true))

Casper states: Av¬C (Alfred is innocent or Casper is not innocent (In mathematics the disjunction "or" doesn't mean only one of the premises can be true. They can both be true and the statement would still be true.))

You take these formalized statements, compare them to every single possible outcome from everyone being innocent to everyone being guilty (there are 3^2=8 of them), and rule out those that don't match the statements and the information that you're given. You're left with one possibility, which is that Beatrice is the only one being guilty, or A^¬B^C, as it could be put.

I hope you had fun! I will surely try doing something like this again in the future.
Edited 2 times - Last edited at 18:30:01 11/01/2016 by Samius
Spyro Fanatic Hunter Gems: 12928
#17 Posted: 18:30:07 11/01/2016
SpyroFanatic.exe has crashed.

[User Posted Image]

I can usually do these puzzles, but not at 2:30 AM.
---
R.I.P. Ra
June 16th 2000 ~ May 3rd 2017
Samius Hunter Gems: 9573
#18 Posted: 18:35:29 11/01/2016 | Topic Creator
Quote: Spyro Fanatic
SpyroFanatic.exe has crashed.

[User Posted Image]

I can usually do these puzzles, but not at 2:30 AM.


Sleep is extremely important for exams. Go to sleep.
Seiki Platinum Sparx Gems: 6150
#19 Posted: 18:35:36 11/01/2016
First, it has to be either Alfred or Beatrice. If both are telling the truth, then it means all 3 are innocent. Yet one is the culprit.
Therefore, Casper is innocent as the culprit is either Alfred or Beatrice.
If Casper is innocent, Alfred is telling the truth.
This means Beatrice is the culprit.

-----
---
Once in my dreams, I rose and soared. No matter how I'm knocked around or beaten down, I will stand up restored.
Spyro Fanatic Hunter Gems: 12928
#20 Posted: 18:38:25 11/01/2016
Quote: Samius
Quote: Spyro Fanatic
SpyroFanatic.exe has crashed.

[User Posted Image]

I can usually do these puzzles, but not at 2:30 AM.


Sleep is extremely important for exams. Go to sleep.


Okay ._. goodnight.
---
R.I.P. Ra
June 16th 2000 ~ May 3rd 2017
Samius Hunter Gems: 9573
#21 Posted: 18:39:35 11/01/2016 | Topic Creator
Quote: Seiki
First, it has to be either Alfred or Beatrice. If both are telling the truth, then it means all 3 are innocent. Yet one is the culprit.
Therefore, Casper is innocent as the culprit is either Alfred or Beatrice.
If Casper is innocent, Alfred is telling the truth.
This means Beatrice is the culprit.

-----


Yeah, that's pretty much it.
darkwolf Diamond Sparx Gems: 7975
#22 Posted: 19:11:18 11/01/2016
[User Posted Image]

Will be back with an answer...
CAV Platinum Sparx Gems: 6430
#23 Posted: 19:25:37 11/01/2016


Thing is that yes partial truths can still be considered lies, but so can partial truths be considered truth. I may have misread but the statement seems to imply that either the entire statement is true or the entire statement is false (and since I felt Alfred was innocent I reasoned Beatrice was as well, since a lie within this logic implies both would be guilty).

-----
Samius Hunter Gems: 9573
#24 Posted: 19:46:10 11/01/2016 | Topic Creator
Quote: CAV


Thing is that yes partial truths can still be considered lies, but so can partial truths be considered truth. I may have misread but the statement seems to imply that either the entire statement is true or the entire statement is false (and since I felt Alfred was innocent I reasoned Beatrice was as well, since a lie within this logic implies both would be guilty).

-----


That's what I thought. But yeah, even though the statement is false, it can have a premise which is true.

Much like, let's say: "There are more chickens on this planet than there are people, and panda bears don't exist."

The first premise is true, but the statement (referring to the entire thing that he said) is false, since the conjunction (In this case "and", though it would work with words like "but", "yet", etc. as well. In math it's just called a conjunction) implies that both premises are true.

It's a technicality, really. In an argument I wouldn't say that a person saying that sorta thing was "completely" wrong, but his statement would still be untrue nonetheless.


-----
Metallo Platinum Sparx Gems: 6419
#25 Posted: 19:49:56 11/01/2016
Filler.


Alfred and Casper's answers cancel each other out, meaning that they are either both innocent or both guilty. Since there's only one guilty person, we know they must both be innocent, and therefore Beatrice is guilty by process of elimination.

I thought this and then checked Samius's answer to confirm.
darkwolf Diamond Sparx Gems: 7975
#26 Posted: 19:54:27 11/01/2016
Okay, I think I got it.

Beatrice is guilty.

If you assume Beatrice is telling the truth, Casper must be guilty. This makes Alfred's statement untrue, which would mean he is lying and is therefore guilty. But if Alfred were guilty, then Casper's statement would be untrue, which makes him guilty.

There's a problem, though. If Casper were guilty, then Alfred would be lying and he would be guilty. That makes Beatrice's statement untrue, which means she is guilty.
Samius Hunter Gems: 9573
#27 Posted: 20:15:40 11/01/2016 | Topic Creator
Quote: Metallo
Filler.


Alfred and Casper's answers cancel each other out, meaning that they are either both innocent or both guilty. Since there's only one guilty person, we know they must both be innocent, and therefore Beatrice is guilty by process of elimination.

I thought this and then checked Samius's answer to confirm.


Then I'm sure you already know you're correct.

Quote: darkwolf
Okay, I think I got it.

Beatrice is guilty.

If you assume Beatrice is telling the truth, Casper must be guilty. This makes Alfred's statement untrue, which would mean he is lying and is therefore guilty. But if Alfred were guilty, then Casper's statement would be untrue, which makes him guilty.

There's a problem, though. If Casper were guilty, then Alfred would be lying and he would be guilty. That makes Beatrice's statement untrue, which means she is guilty.


You are also correct, though your reasoning sounds a bit weird at the end there. I'm sure you just couldn't put it in the right words atm.
HIR Diamond Sparx Gems: 9034
#28 Posted: 21:01:26 11/01/2016
Beatrice is the guilty party.

Casper offers an "either/or" scenario, suggesting Alfred's innocent (and telling the truth) OR he's guilty. Both parts can't be true, because if he's guilty, then Alfred is innocent. But innocent members ALWAYS tell the truth. Which would make his statement of Casper's innocence a contradiction.

Similarly, if Alfred were guilty, then Casper and Beatrice are telling the truth. But their statements both refer to Alfred's innocence in order to be true, which would create ANOTHER contradiction.

Therefore, Alfred HAS to be innocent. Which makes his statement true. Therefore, Casper must also be innocent. This scenario DOES work because Alfred's innocence satisfies one part of Casper's "either/or" scenario, which is good enough.

This leaves Beatrice as the culprit. She's lying about her own innocence, and that makes her whole statement false.


[User Posted Image]

(I forgot how much I hate logic in math...)
---
Congrats! You wasted five seconds reading this.
Samius Hunter Gems: 9573
#29 Posted: 21:10:51 11/01/2016 | Topic Creator
Quote: HIR
Beatrice is the guilty party.

Casper offers an "either/or" scenario, suggesting Alfred's innocent (and telling the truth) OR he's guilty. Both parts can't be true, because if he's guilty, then Alfred is innocent. But innocent members ALWAYS tell the truth. Which would make his statement of Casper's innocence a contradiction.

Similarly, if Alfred were guilty, then Casper and Beatrice are telling the truth. But their statements both refer to Alfred's innocence in order to be true, which would create ANOTHER contradiction.

Therefore, Alfred HAS to be innocent. Which makes his statement true. Therefore, Casper must also be innocent. This scenario DOES work because Alfred's innocence satisfies one part of Casper's "either/or" scenario, which is good enough.

This leaves Beatrice as the culprit. She's lying about her own innocence, and that makes her whole statement false.


[User Posted Image]

(I forgot how much I hate logic in math...)


That is correct.

I quite like it myself (so far, at least).
Gage Platinum Sparx Gems: 6654
#30 Posted: 21:26:05 11/01/2016
I did it.
---
Got it Memorized?
Greeble Emerald Sparx Gems: 4431
#31 Posted: 13:55:13 13/01/2016
My head hurts smilie
---
^ You all know it's true
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