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An entry in the 19th fortnightly challenge...


Trutham-And-Ly, you may remember, is a small town in the north of Logistan. It is divided into two districts, Trutham and Ly, separated by a small stream. Truthamers always tell only the truth, and Lyers only tell lies.

Years ago, the people of Ly had an interesting disability. But the Trutham-And-Ly of today is populated with roughly equal numbers of residents in both districts, all of whom can and do express themselves quite readily in all the same ways as people anywhere else might — talking, writing, emailing, texting, and so on — except that they all unfailingly either only lie or only tell the truth, in accordance with the district in which they live.


 You are a resident of Trutham-And-Ly, and it is Halloween night. You are in a room of your house some distance from the door as you hear the doorbell ring, your first trick-or-treaters of the night!

 As you begin walking to answer your door, from outside you hear a girl's voice say, "I hope they're not giving away gum, I hate gum."
 A boy's voice responds, "You're such a liar. You were chewing gum earlier!"
 A girl's voice—you can't tell if it is the first voice or not—says, "Shut up, Fred—there are no Lyer girls in this group."
 "Ignore her, Fred. You can't believe a single thing these girls say," says another boy.
 "You shut up too, E--"
 Yet another boy cuts her off. "Quiet, all of you be. Coming to the door, they are."

 You arrive at the door and open it to see a clown, Dracula, an angel, a cowgirl, Yoda, and a zombie, holding out their bags and shouting out a loud chorus of "Trick Or Treat!"s.
 The cowgirl gestures at your Halloween décor and says, "I really like your decorations!"
 The clown, the tallest of the group, tells the others, "Don't crowd the doorstep!" as he pulls them back slightly. He asks, "Is it ok if I pick for everyone? We all like different candy and I know what everyone would want."
 Two boys start saying in unison, "Don't forget ...!"
 The clown interrupts them. "Yes, I know all about your allergies! Sheesh!", he says.

 The clown starts rustling through the candy in your bowl. "Oooh, Snickers are my favorite, I'll take one of those. And... let's see... something with toffee for Anne; no nuts of any kind for Edward; and no chocolate for Fred...."
 "I'd love a Butterfinger if there are any," moans the zombie zombiely.
 "Do they have any Almond Joys?" asks the cowgirl.
 "If they do, give one to Edward!" smirks the angel, sticking out her tongue at Yoda.
 "Now, now, let's not kill anyone tonight," the cowgirl chuckles.
 Dracula snorts, "Edward's such a Lyer anyway. Would we even miss him?" earning him jabs and playful swats from the angel, the zombie, the cowgirl and Yoda.

 Meanwhile, the clown selects a Snickers bar, a Heath bar, a roll of Smarties, a Butterfinger bar, a packet of Gummi Worms, and an Almond Joy bar from the bowl.
 He drops the Snickers into his own bag.
 Into Yoda's bag, the Smarties he drops.
 The Gummi Worms go into Dracula's bag.
 You hear three more swishes as the clown turns around and deposits the remaining goodies into the other three children's bags.
 He says a cheery "Thank you!" to you, and the others add their own over-sugared thanks to his.

 The group turns and starts walking toward the next house.
 "Thanks, Billy," you hear a girl's voice say as they move beyond the light of your front door.
"There's some 'chocolate' on your nose there, Cowgirl," retorts one of the boys.
 Another girl's voice says, "I can't believe you got me an Almond Joy. Nobody under, like, 60 even eats those. I think they're disgusting!"
 A boy's mock-exasperated voice responds, 'Oh hush, ya big Lyer. Seriously, why do we even hang out with you?!"
 "You tell her, Billy!" a girl giggles in response, her voice barely carrying back to reach you as the group moves out of earshot.

 You close your door with a smile and a shake of your head, and head back inside.


HINT because this is leading people astray:

"Do they have any Almond Joys?" is a simple question, nothing more.
The cowgirl never says she likes them or that she wants one — nor the opposite.
be mad if you want; this was intentional misdirection, but I guess it went a little too far.

  • What candy did David get?
  • Did the cowgirl really like your Halloween decorations?
    (Please provide an explanation for your answers!)

A few assumptions you can make:
- You can safely assume the cowgirl is a female.
- You can also assume names are gender-normal.
- Nobody is ever called by an incorrect name (nor interrupted before doing so.) Whatever other peculiarities they have, both Truthamers and Lyers call each other by their right names. (But saying "Your name is Foo." or "You are a Lyer" would fall within their truth-telling or lying standards.)
- Questions (and requests) are not statements, so are neither true nor false and thus unrestricted.

——CORRECTION——
The line of the story in bold was accidentally omitted when this was originally edited for posting. With this line missing, the accepted answer was the only answer possible to give. With the line restored, the puzzle can now be fully completed to arrive at my intended solution. Other answers arrived at an incorrect solution for which this line's presence or absence should not have mattered, but I apologize for the error in any case; I should have caught it.

Thanks to Anon for the original conception of Trutham-And-Ly.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Aza Nov 2 '16 at 0:56
  • $\begingroup$ I've restored the missing line, and noted that it was not there when originally posted. I was initially hesitant to do this, but it seems like the right thing to do. $\endgroup$ – Rubio Nov 3 '16 at 11:22
  • $\begingroup$ Seriously? This is getting absurd. Your new line allows you to confirm that "Carol" is almond joy girl but we already knew that. Even if you meant to imply the angel or cowgirl had eaten chocolate already while the other hadn't, the "chocolate" can be taken to be a metaphor so neither a true or false statement. $\endgroup$ – kaine Nov 3 '16 at 20:27
  • $\begingroup$ oh what the ... lol. I grabbed an old version of that line. i should quit while I'm less behind. thanks for pointing that out, the right word is now there. $\endgroup$ – Rubio Nov 3 '16 at 21:24
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Trying again. Working through line by line...

First girl says she hates gum and a boy responds that she's a liar (clearly one is a liar). Then a girl (possibly the first) calls the boy Fred and says there are no girl Lyers.
Another boy (Edward) says you can't believe anything the girls say (so either he is a Lyer or both girls are)
If both girls are Lyers, then Fred and Edward are truth tellers.
If not, it's some various combination I'll look at later...
Another boy (who is seemingly Yoda, probably OP's trick) says that you are coming to the door (truth)

Cowgirl compliments decorations (Question)
Clown says he will pick for everyone and knows what they want Two boys speak up about allergies and the clown interrupts saying he knows (seemingly truth)

Clown says snickers are his favorite, toffee (heath bar) for Anne, no nuts for Edward, no chocolate for Fred
Zombie requests butterfinger
Cowgirl asks if there are any Almond Joys
Angel says to give one to Edward and sticks tongue out at Yoda (Edward is Yoda?)
Dracula calls Edward a Lyer (So either Dracula or Edward is a Lyer)

Clown gets Snickers
Yoda gets Smarties
Dracula gets Gummi Worms
Zombie gets Butterfinger (because Clown seems to be honest and do requests)
Anne gets Heath (toffee)
Carol gets Almond Joy (only candy left)
Edward and Fred have to be Yoda and Dracula as every other candy has Chocolate or nuts
Dracula called out Edward so he must be Fred, meaning Edward is Yoda

Billy is the Clown as the kids thanked him
So David must be the Zombie
A girl complains about getting Almond Joy and Billy calls her a Lyer

Deductions...

Because Billy is a truth teller the girl must be a Lyer. Edward said both girls were Lyers, and Fred said Edward is a Lyer and one of the girls is a Lyer. If Fred is a Lyer, then the girl would be a truther and Edward would be a truther, but Edward can't be a truther if at least one of the girls is a truther. Therefore Fred must be a truther and Edward is a Lyer, and so both girls can't be lyers. And because Billy and Fred each called a girl a Lyer, one of them must be (and they must be the same girl)

So the cowgirl...

Can't be determined. We know that one girl is the Angel and the other girl is the Cowgirl.
We know one girl is a Lyer and the other is not.
For the girl that is a Lyer, the only statements we know from her that are lies are "I hate gum", "There are no Lyer girls", and the Almond Joy. About the Almond Joy, she is either lying about not liking them, or about receiving one. (I can't believe you got me an Almond Joy -> I believe you got me an Almond Joy / I can't believe you didn't get me an Almond Joy). In the first case, Carol would be the liar, in the second Anne would be the liar. We can't determine which costume either girl is wearing though.
All we know about the cowgirl is she said she likes your decorations, she asked if there is an Almond Joy, and she said not to kill anyone tonight.
All we know about the angel is she joked about giving the Almond Joy to Edward


Old answer below, leaving for posterity.

So...

Anne is the Angel with the Heath bar from Trutham
- She told the truth about there being an Almond Joy

Billy is the Clown with the Snickers from Trutham
- He told the truth about the candy and about Cindy being a Lyer

Cindy is the Cowgirl with the Almond Joy from Ly
- She lied about the Almond Joy

David is the Zombie with the Butterfinger from Trutham
- Requested Butterfinger and told the truth about the owner coming to the door (in a Yoda voice I guess to poke fun at Edward?)

Edward is the Yoda with the Smarties from Ly
- He lied implying both girls were Lyers

Fred is the Dracula with the Gummi Worms from Trutham
- He told the truth calling Edward a Lyer. This also means the very first girl was Cindy lying about gum, and that Cindy told him and Edward to shut up

Which comes to...

The same answer as MMAdams and Sconibulus that David got the Butterfinger and the Cowgirl lied about your decorations being nice but with slightly different pairings for where they're from. I'm assuming one of the statements used to determine a Truth/Lie is incorrect which is kind of confusing that some types of statements are acceptable but others aren't.

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  • $\begingroup$ Sorry, your answer is not correct. There's a bit of intentional misdirection in this puzzle, and you've fallen victim to it. Look closely and make sure everything fits :) $\endgroup$ – Rubio Oct 31 '16 at 20:11
  • $\begingroup$ Ah good puzzle. I admit I rushed and ending up missing some contradictions. $\endgroup$ – Ryan Smith Oct 31 '16 at 20:37
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    $\begingroup$ Updated answer. Didn't find anything different from the other answers so I'm not sure if there is a fault in the question? I worked through all of the reasoning line by line if it helps to find what went wrong. $\endgroup$ – Ryan Smith Oct 31 '16 at 22:12
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    $\begingroup$ @Rubio Aaaaaaaaarrrrrrrrrrrrgggggggghhhhhhh. Probably a good idea to double-check stuff like that, especially when several of us spent a lot of time super-carefully parsing the story assuming we hadn't quite found the key yet. I really like this idea of combining the liars and logic puzzles, it just needed a bit tidier execution. $\endgroup$ – Dan Russell Nov 2 '16 at 16:53
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    $\begingroup$ @DanRussell Yeah, trust me I'm pretty mad at myself for not spotting the error. It's one of those cases where I know what I put in there--even though it's not actually in there. In any case, Ryan arrived at the correct conclusions for the puzzle as posted, and I don't believe anyone else did; if my intent had been to make the final question's answer undecidable (and at an earlier point in development I had thought to do just that), he was the only one who got there. But good efforts from everyone, and I hope you enjoyed the novel combination and had a bit of fun working through it. $\endgroup$ – Rubio Nov 2 '16 at 17:00
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The trick-or-treaters, their costumes, candies, and origins are in the following non-table:

Edward=Yoda=Smarties=Truthamite
Fred=Dracula=Gummi Worms=Lyer
Billy=Clown=Snickers=Truthamite
David=Butterfinger=Zombie=Truthamite
Cindy?=Cowgirl=Almond Joy=Lyer
Anne=Angel=Heath Bar=Truthamite

What candy did David have?

Butterfinger

Did she like your decorations?

Aww hell no. Maybe you should have done more than just put out an uncarved plastic pumpkin?

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  • $\begingroup$ Trutham residents are, apparently, called Truthamers. The missing girl's name is actually Carol (not that you can get that from the puzzle), but Cindy was a pretty insightful guess. You and MMAdams both arrived at the same set of answers, and both have the same error(s). I need to review and make sure I didn't mess something up, but I think there's an unwarranted assumption being made somewhere. $\endgroup$ – Rubio Oct 31 '16 at 20:42
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    $\begingroup$ I can see how Almond Joy goes with Lyer and Heath Bar goes with Anne. But same question as to MMAdams: how did you resolve the rest of the Anne/Cindy associations? Meaning, I can get to Truthamer-Anne-HeathBar and Lyer-Cindy-AlmondJoy, but Cowgirl vs Angel? $\endgroup$ – Dan Russell Oct 31 '16 at 20:43
  • $\begingroup$ how did you come to the conclusion that Fred was a Lyer? The rest I agree with you on 100% though. $\endgroup$ – MMAdams Oct 31 '16 at 20:44
  • $\begingroup$ @MMAdams Fred's a Lyer because he's Dracula, and Dracula says that Edward's a Lyer, which is false. $\endgroup$ – Dan Russell Oct 31 '16 at 20:45
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    $\begingroup$ @Sconibulus Yeah, I guess it's hard to know what's implied by each line. So basically a Lyer can say: "Do they have any Almond Joys? Would you get me one please? Would you put it in my bag? ... I can't believe you got me that, it's disgusting!" $\endgroup$ – Dan Russell Oct 31 '16 at 20:51
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My solution

Things we can find from the clues are -

The girls get almond joy and heath.
The clown, zombie, yoda, and Dracula are male.
The clown cannot be lying as he says "I'll take the snickers" and does. Fred and Ed by necessity get the only hypoallergenic snacks.
Yoda and Dracula get the hypoallergenic snacks so are Fred and Ed.
Dracula call Ed a liar so is not a Ed. Fred is Drac and Ed is yoda.
Only one of Fred or Ed are lying.
If Fred is lying, another male is lying (as Fred says girl 1 lies and another says both lie).
As the only snack left is the butterfinger, the only male left, the zombie, gets that. He is telling the truth.

Therefore,

exactly three boys tell the truth and one boy is a liar.
Edward is, therefore, a liar. Fred tells the truth.
Therefore one but not both of the girls is lying.

Also,

Almond Joy lies assuming the clown plays fair. Billy says she lies, so Billy tells the truth (which we already knew). Anne tells the truth. Almond Joy is "Carol" and a liar.

So:

- Ed = Yoda = smarties = Liar (which makes no sense as we hear "yet another boy" in yoda's voice tell the truth)
- Fred = Dracula = gummi = True
- zombie = butterfinger = true (name unknown)
- Billy = true
- clown = snickers = true
- David = true (assumption as only 1 boy lies)
- Anne = heath = true
- Carol = almond joy = liar

Circumstantial evidence which turns out true:

The angel makes a face at Yoda when referring to Edward.
Edward talks just before a girl refers to E-.

Contradictory circumstantial evidence:

Someone in Yoda's voice makes a truthful statement.

We know that

Now either Carol or Anne is a liar and either Billy or David are the clown.
The only evidence as to who are Billy and David is that someone thanks Billy and Billy correctly calls almond girl a liar. As both Billy and David are truth tellers, the latter part is useless. I presume, therefore, that the clown is Billy as he is worth thanking.

That means

David is the zombie so gets a butterfinger.

There is no way to determine the bonus question as

there is nothing to distinguish the cowgirl and the angel. Neither are identified as making any statements that can be either true or false. No distinguishing characteristics are given to either.


After many revisions the bonus question can now be answered. The new line calls the "Thanks Billy" girl "Cowgirl". "Another Girl" then discusses the Almond Joy. As the Almond Joy girl is lying:

the Almond Joy girl is not the cowgirl which means she is the angel. That means the angel is the liar and the cowgirl is not. Therefore: Cowgirl = Anne = Heath = Truth; Angel = Carol = Almond = Liar. The Cowgirl liked you decorations.

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  • $\begingroup$ I am answering because I ignore OP's hint and still conform to the answer his hint seemingly dissuades. Are any of my assumptions wrong? $\endgroup$ – kaine Nov 1 '16 at 19:32
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    $\begingroup$ Hmm. "Yeah, give one to Edward!" was not intended to mean "Yes, there are some, give one to Edward!". The wording in the puzzle has been changed to avoid this misinterpretation. Your analysis went astray at that point but had not made any untrue conclusions up until there (I'm not clear on some of the reasoning that got you there, but it ended in the right place). The girl's name we didn't hear in the story starts with C (you should be able to tell why); her name is in fact Carol, if anyone cares. :) $\endgroup$ – Rubio Nov 1 '16 at 19:48
  • $\begingroup$ @Rubio I assumed Emma only so I could not glean untrue info from "E-" by assuming it means Edward. Thank you. $\endgroup$ – kaine Nov 1 '16 at 19:50
  • $\begingroup$ @Rubio I also assumed that "Yeah" to "Are there any Almond Joys?" meant the Angel was a Truthamer, since there were indeed Almond Joys there. $\endgroup$ – Dan Russell Nov 1 '16 at 19:55
  • $\begingroup$ @DanRussell Whoops. Sorry then for leading you folks astray. In the story she doesn't know what's in the bowl because she's not looking in it, only the clown is, so her "Yeah" wasn't supposed to be an answer to the cowgirl. I understand the confusion and fixed it when I saw kaine went sideways there. Mea culpa! $\endgroup$ – Rubio Nov 1 '16 at 19:59
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David got a

Butterfinger

Our six trick-or-treaters are Anne, Billy, David, Edward, Fred, and another girl.

Anne is

The angel. Anne is given a Heath bar, since it has Toffee in it.

The other girl is

The cowgirl, and gets an Almond Joy, which she says she doesn't like.

Billy is

The clown, as one of the girls thanks him for giving out the candy. He gives himself a Snickers.

Edward is

Yoda, since the Angel sticks her tongue out at him when making fun of Edward. He gets a Smarties.

Fred is

Dracula, because Fred can't eat chocolate, and since we have established Yoda is Edward, the only other non chocolate candy were the Gummy worms given to Dracula.

David is

The Zombie, and he was given the Butterfinger, the last remaining candy.

Did the cowgirl really like your decorations?

NO. It is established that the cowgirl is a Lyer, since she specifically asks if there are almond joys and then complains that she finds them disgusting when she is given one. Therefore she did not like your decorations.

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  • $\begingroup$ I probably shouldn't have said "Bonus Question" for the bonus question - it's part of the puzzle. Editing to fix that. Do you have an answer for that part? $\endgroup$ – Rubio Oct 31 '16 at 20:27
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    $\begingroup$ How did you figure out who was the angel and who was the cowgirl? $\endgroup$ – kaine Oct 31 '16 at 20:36
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    $\begingroup$ Yoda can't be edward can he? -Boy: "all girls are liars, Fred" Girl:"Shut up E- (Edward)" ANOTHER Boy: "protagonist is coming to door" (in yoda's voice) $\endgroup$ – kaine Oct 31 '16 at 20:49
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    $\begingroup$ @Sconibulus Nobody is ever called by an incorrect name (nor interrupted before doing so.) Whatever other peculiarities they have, both Truthamers and Lyers call each other by their right names. (But saying "Your name is Foo." or "You are a Lyer" would fall within their truth-telling or lying standards.) $\endgroup$ – Rubio Oct 31 '16 at 21:00
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    $\begingroup$ @Rubio My point was that what follows the comma doesn't have to be a name at all, in my case, it was an exclamatory interjection. Since you're the OP though, I guess you intended it to be a name, and so I'll rework with that assumption. $\endgroup$ – Sconibulus Oct 31 '16 at 21:02

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