In the small town of Smullyville, the inhabitants can be classified as liars and truthers. Many things go on in town, some mundane and others extraordinary. I have some puzzles regarding their lives. See if you can figure them out. I will be keeping score. Only one answer for each person for each puzzle and only the first correct answer scores.

In town last week there was a race between Allie, Barbie, Chuck, and Doug. When asked about the race, this is what they had to say...

Chuck said "Barbie came in second."
Doug said "Chuck came in second."
Chuck said "Allie came in second."
Allie said "Barbie came in last."
Barbie said "Doug came in third."

The winner told the only truth and everyone else told only lies. In what order did they actually finish?

2. difficulty: very easy

John, the barber opened shop recently. So now there are two barbers in town, he and Edward. John has a good-looking hair cut. Edward's looks awful. If visiting town, which should you choose and why?

3. difficulty: easy
Two of the citizens of Smullyville — Raj and Natasha — were talking together. Raj observed, "At least one of us is a liar."

The question is, what are Raj and Natasha (each is a liar or a truther)?

4. difficulty: easy
Patrick and Patricia Partridge are brother and sister. Patrick has as many brothers as sisters. Patricia has twice as many brothers as sisters. How many brothers and sisters are in their family?

5. difficulty: rather hard
There used to be only one barber, Edward. His sign outside the shop used to read "I shave every man in town who does not shave himself, and nobody else." Somehow everyone in town figured out that he was a liar. How?

6. difficulty: easy
The twin grandfather clocks at Jenny's Diner begin to chime at exactly the same time every hour. The one on the left chimes faster than the one on the right. In fact, it chimes three times for every two chimes from the one on the right. At a particular hour every day (twice a day in fact), the one on the left finishes chiming and then the one on the right chimes two more times. What time is that?

5: Two options
a) Another man in town is unshaved.
b) Edward is shaved. In which case his statement isn't true, as he would have shaved a man who does shaved himself.

6: Assuming that the chimes happen with the same interval for both clocks, then whatever time the clock on the left chimes 4 times. (Presumably when the left clock shows 4 o'clock, although you don't really have enough info to know whether that is the actually the correct time or not)

For number 5, Napthali, we are looking for a contradiction without wiggle room. An unshaven man could claim that he has simply not got around to it. As for Edward himself being shaved, I think you are on the right track. Feel free to answer this one again.

I added a clause into number 6 to make it read more clearly. See if that helps. Feel free to answer this one again as well.

A stranger (not from town) came across three of Smullyville's citizens — Wanda, Anwar, and Levy. Wanda volunteered this information: "Anwar and Levy are of the same type (liars or truthers)." The stranger then asked Levy, "Are Wanda and Anwar of the same type?"

What was Levy's answer? Explain it or no point since it's a 50/50 guess.

8. difficulty: hard

Smullyville is infested with werewolves. During the daytime it's hard to tell which folks are werewolves since they just go about their business. In fact, anyone could be. In this puzzle, three folks from Smullyville make statements:

Andy: Corinne is a werewolf.
Bruce: I am not a werewolf.
Corinne: At least two of us are liars.

In fact, exactly one of the three townspeople is a werewolf. For the point, you have to answer both of these correctly.

Is the werewolf a truther or a liar?
Which of the three townspeople is definitely not a werewolf?

A stranger (not from town) came across three of Smullyville's citizens — Wanda, Anwar, and Levy. Wanda volunteered this information: "Anwar and Levy are of the same type (liars or truthers)." The stranger then asked Levy, "Are Wanda and Anwar of the same type?"

What was Levy's answer? Explain it or no point since it's a 50/50 guess.

Case 1: Wanda tells the truth; Anwar and Levy lie.
Then Levy would say that Wanda and Anwar are the same type (which is false).

Case 2: All three tell the truth.
Levy says that Wanda and Anwar are the same type, which they are.

Case 3: Wanda lies, Anwar's a truther, and Levy lies.
Levy says they're the same type, which they aren't.

Case 4: Wanda lies, Anwar lies, Levy's a truther.
Levy says that Wanda and Anwar are the same type, which is true.

6. difficulty: easy
The twin grandfather clocks at Jenny's Diner begin to chime at exactly the same time every hour. The one on the left chimes faster than the one on the right. In fact, it chimes three times for every two chimes from the one on the right. At a particular hour every day (twice a day in fact), the one on the left finishes chiming and then the one on the right chimes two more times. What time is that?

6:00. The one on the left will finish after the one on the right has done four chimes.

5. Edward is shaven. This means that either he shaves himself, which would violate the statement (he shaves himself, but he doesn't shave people who shave themselves), or there is another barber in town, which is false.

for clarity's sake: or Edward is unshaven, which implies that he doesn't shave himself, and that he does shave himself b/c he doesn't shave himself - contradiction

8. We can't conclude for sure who is a werewolf, and for sure who is a liar. We do however know that
- the werewolf is a liar, and
- Andy is not a werewolf.

If A is a truther:
-C is a werewolf.
-B is a truther.
-C is a liar.

If A is a liar:
-C is not a werewolf.
-C must be a truther; if she weren't, then there could be only one liar, her.
--This means that B is a liar, and a werewolf.

At any rate, I have to get better at parsing these responses. I looked at supermo's answer which is quite similar to Naphtali's and on reflection, I think Naphtali got it. The actual answer is simply the sign can not possibly tell the truth whether Edward shaves himself or not. Either way he is lying. So it is the sign itself that gives him away. But the answer(s) given seem to imply that same thing.

At any rate, I have to get better at parsing these responses. I looked at supermo's answer which is quite similar to Naphtali's and on reflection, I think Naphtali got it. The actual answer is simply the sign can not possibly tell the truth whether Edward shaves himself or not. Either way he is lying. So it is the sign itself that gives him away. But the answer(s) given seem to imply that same thing.

Opinions? Nap or no point for anyone?

Give it to Nap, he got it correct, after all.

Also consider rephrasing the question, say, have a blind individual hear someone read the sign and conclude that Ed is a liar. That way Ed's status of shaven/unshaven is insignificant.

8 is solved. Nice, supermo. TheEndIsNear, you have an incorrect assumption that lead you to conclude that "B is not W and T" which we can not actually know. I was not sure what to do there, except that you did not really answer all the questions, so I can not award you the point. Here is the full explanation.

1. The werewolf is a liar.
2. The only person that we know for sure is not a werewolf is Andy.

Explanation: We know that Corinne is either a truther or a liar.

Case 1: Suppose that Corinne is a truther.

Then her statement is true, and there are indeed at least two liars in the group. But since Corinne is a truther, this implies that both Andy and Bruce must be liars. This means in particular that Bruce's statement is false, and therefore he is a werewolf, in fact the one and only werewolf in the group. We see that in this case the werewolf is a liar, namely, Bruce.

Case 2: Suppose on the other hand that Corinne is a liar.

Then her statement is false, and there is at most one liar in the group. But since Corinne is a liar, this implies that both Andy and Bruce must be truthers. This means in particular that Andy's statement is true, and therefore Corinne is indeed a werewolf, in fact the one and only werewolf in the group. Thus, in this case too, the werewolf is a liar, namely, Corinne.

Since in either case the werewolf turns out to be a liar, we conclude that the werewolf is indeed a liar. (filthy beasts, can't trust 'em!)

We have just analyzed the only two possibilities as far as Corinne is concerned. In the first case, Bruce turns out to be the one and only werewolf; in the second, it is Corinne who is the one and only werewolf. We may be certain therefore that, regardless of whether Corinne is a truther or a liar, Andy is definitely not the werewolf.

One day, three of Smullyville's citizens were sitting in the park when the conversation turned to the day of the week.

Willie said "Zach is a liar."
Xavier then said "That's true."
Then Yolanda said "The name of the day does not have the letter 's' in it."
Finally Zachary said "It's Friday."

Exactly three of these people are truthers. What day of the week was it?

10. difficulty: kinda hard

Professor Schtiggenzlufen at Smullyville College has been working on his time machine for years. Rumor has it that he has finally perfected it. Everyone knows that he will set the target date of his maiden voyage for one of the following:

1600
1650
1700
1750
1800
1850

Yesterday, a reporter for the local newspaper interviewed two of his assistants about that date. This is what they said.

Assistant #1 said: If the year is before 1777 then #2 tells the truth.
Assistant #2 said: The year is not after 1742.
Then, assistant #1 said: The year is not 1850.
Then assistant #2 said: That's not true.

The interview is accurate and the reporter is a truther. The assistants may be either truthers or liars. What is the date the time machine is set for?

Private Mod Note
():

Rollback Post to RevisionRollBack

Brainstorm Schmainstorm

To post a comment, please login or register a new account.

Top scorers:

5 supermoo9999

4 Naphtali

2 BronYAur

2 Aurora Illumina

1. difficulty: mediumIn town last week there was a race between Allie, Barbie, Chuck, and Doug. When asked about the race, this is what they had to say...

Chuck said "Barbie came in second."

Doug said "Chuck came in second."

Chuck said "Allie came in second."

Allie said "Barbie came in last."

Barbie said "Doug came in third."

The winner told the only truth and everyone else told only lies. In what order did they actually finish?

2. difficulty: very easyJohn, the barber opened shop recently. So now there are two barbers in town, he and Edward. John has a good-looking hair cut. Edward's looks awful. If visiting town, which should you choose and why?

3. difficulty: easyTwo of the citizens of Smullyville — Raj and Natasha — were talking together. Raj observed, "At least one of us is a liar."

The question is, what are Raj and Natasha (each is a liar or a truther)?

4. difficulty: easyPatrick and Patricia Partridge are brother and sister. Patrick has as many brothers as sisters. Patricia has twice as many brothers as sisters. How many brothers and sisters are in their family?

I've got two different answers that sem to me to satisfy the given information.

IF Allie is telling the truth then the order is

(1st) Allie, Doug, Chuck, Barbie (last)

IF Doug is telling the truth then the order is

(1st) Doug, Chuck, Barbie, Allie (last)

2: You should go to Edward, because he cut John's hair.

At any rate, those are correct answers. In this case, I had better award the point twice.

4: There are 3 girls and 4 boys in the family (including Patrick and Patricia)

5. difficulty: rather hardThere used to be only one barber, Edward. His sign outside the shop used to read "I shave every man in town who does not shave himself, and nobody else." Somehow everyone in town figured out that he was a liar. How?

6. difficulty: easyThe twin grandfather clocks at Jenny's Diner begin to chime at exactly the same time every hour. The one on the left chimes faster than the one on the right. In fact, it chimes three times for every two chimes from the one on the right. At a particular hour every day (twice a day in fact), the one on the left finishes chiming and then the one on the right chimes two more times. What time is that?

a) Another man in town is unshaved.

b) Edward is shaved. In which case his statement isn't true, as he would have shaved a man who does shaved himself.

6: Assuming that the chimes happen with the same interval for both clocks, then whatever time the clock on the left chimes 4 times. (Presumably when the left clock shows 4 o'clock, although you don't really have enough info to know whether that is the actually the correct time or not)

I added a clause into number 6 to make it read more clearly. See if that helps. Feel free to answer this one again as well.

7. difficulty: mediumA stranger (not from town) came across three of Smullyville's citizens — Wanda, Anwar, and Levy. Wanda volunteered this information: "Anwar and Levy are of the same type (liars or truthers)." The stranger then asked Levy, "Are Wanda and Anwar of the same type?"

What was Levy's answer? Explain it or no point since it's a 50/50 guess.

8. difficulty: hardSmullyville is infested with werewolves. During the daytime it's hard to tell which folks are werewolves since they just go about their business. In fact, anyone could be. In this puzzle, three folks from Smullyville make statements:

Andy: Corinne is a werewolf.

Bruce: I am not a werewolf.

Corinne: At least two of us are liars.

In fact, exactly one of the three townspeople is a werewolf. For the point, you have to answer both of these correctly.

Is the werewolf a truther or a liar?

Which of the three townspeople is definitely not a werewolf?

Standard:

UBU/B TezzeretBU

WWW QuestW

RMetal GoblinsR

Legacy:

UCounterTopU

thanks to DarkNightCavalier at Heros of the Plane for the sig

Standard:

UBU/B TezzeretBU

WWW QuestW

RMetal GoblinsR

Legacy:

UCounterTopU

thanks to DarkNightCavalier at Heros of the Plane for the sig

Case 1: Wanda tells the truth; Anwar and Levy lie.

Then Levy would say that Wanda and Anwar are the same type (which is false).

Case 2: All three tell the truth.

Levy says that Wanda and Anwar are the same type, which they are.

Case 3: Wanda lies, Anwar's a truther, and Levy lies.

Levy says they're the same type, which they aren't.

Case 4: Wanda lies, Anwar lies, Levy's a truther.

Levy says that Wanda and Anwar are the same type, which is true.

Levy will always answer yes to the question.

Official Quizmaster of The Crafters!

Follow Lasersharp on Facebook

before actually doing a full thing, just going by guesstimation:

C is W and L

B is not W and T

A is T and not W

A is the A person

B is the B person

C is the C person

W is werewolf

T is truther

L is Liar

6:00. The one on the left will finish after the one on the right has done four chimes.

Official Quizmaster of The Crafters!

Follow Lasersharp on Facebook

for clarity's sake:

or Edward is unshaven, which implies that he doesn't shave himself, and that he does shave himself b/c he doesn't shave himself - contradiction- the werewolf is a liar, and

- Andy is not a werewolf.

If A is a truther:

-C is a werewolf.

-B is a truther.

-C is a liar.

If A is a liar:

-C is not a werewolf.

-C must be a truther; if she weren't, then there could be only one liar, her.

--This means that B is a liar, and a werewolf.

Well, done lady or something...

At any rate, I have to get better at parsing these responses. I looked at supermo's answer which is quite similar to Naphtali's and on reflection, I think Naphtali got it. The actual answer is simply the sign can not possibly tell the truth whether Edward shaves himself or not. Either way he is lying. So it is the sign itself that gives him away. But the answer(s) given seem to imply that same thing.

Opinions? Nap or no point for anyone?

Give it to Nap, he got it correct, after all.

Also consider rephrasing the question, say, have a blind individual hear someone read the sign and conclude that Ed is a liar. That way Ed's status of shaven/unshaven is insignificant.

1. The werewolf is a liar.

2. The only person that we know for sure is not a werewolf is Andy.

Explanation: We know that Corinne is either a truther or a liar.

Case 1: Suppose that Corinne is a truther.

Then her statement is true, and there are indeed at least two liars in the group. But since Corinne is a truther, this implies that both Andy and Bruce must be liars. This means in particular that Bruce's statement is false, and therefore he is a werewolf, in fact the one and only werewolf in the group. We see that in this case the werewolf is a liar, namely, Bruce.

Case 2: Suppose on the other hand that Corinne is a liar.

Then her statement is false, and there is at most one liar in the group. But since Corinne is a liar, this implies that both Andy and Bruce must be truthers. This means in particular that Andy's statement is true, and therefore Corinne is indeed a werewolf, in fact the one and only werewolf in the group. Thus, in this case too, the werewolf is a liar, namely, Corinne.

Since in either case the werewolf turns out to be a liar, we conclude that the werewolf is indeed a liar. (filthy beasts, can't trust 'em!)

We have just analyzed the only two possibilities as far as Corinne is concerned. In the first case, Bruce turns out to be the one and only werewolf; in the second, it is Corinne who is the one and only werewolf. We may be certain therefore that, regardless of whether Corinne is a truther or a liar, Andy is definitely not the werewolf.

More puzzles coming tomorrow perhaps.

9. difficulty: mediumOne day, three of Smullyville's citizens were sitting in the park when the conversation turned to the day of the week.

Willie said "Zach is a liar."

Xavier then said "That's true."

Then Yolanda said "The name of the day does not have the letter 's' in it."

Finally Zachary said "It's Friday."

Exactly three of these people are truthers. What day of the week was it?

10. difficulty: kinda hardProfessor Schtiggenzlufen at Smullyville College has been working on his time machine for years. Rumor has it that he has finally perfected it. Everyone knows that he will set the target date of his maiden voyage for one of the following:

1600

1650

1700

1750

1800

1850

Yesterday, a reporter for the local newspaper interviewed two of his assistants about that date. This is what they said.

Assistant #1 said: If the year is before 1777 then #2 tells the truth.

Assistant #2 said: The year is not after 1742.

Then, assistant #1 said: The year is not 1850.

Then assistant #2 said: That's not true.

The interview is accurate and the reporter is a truther. The assistants may be either truthers or liars. What is the date the time machine is set for?