W and X must both be truthers, since they can't both be liars. Therefore Z is a liar and it's not Friday, and since Y is a truther, the day can't have an 's' in it. Monday is the only day remaining.
10. 1800.
Assume 1 is a liar:
-2 is a truther (from the second set of comments)
--The year isn't after 1742. (from 2's first comment)
But this means the year is before 1777, and 2 is telling the truth. This means 1's first statement is true, and he isn't a liar.
(Note that we also have the contradiction that the year isn't after 1742 and is 1850. Whatever floats your boat.)
1 is a truther:
-2 is a liar (again the second set)
--The year isn't 1850.
--The year is after 1742.
--Since 1 is a truther, the first part of his conditional 'the year is before 1777' must be false.
---This means that the year is 1777 or later.
Our only remaining option is 1800.
At the Collins house, siblings Chuck, Biff and Rachel were being questioned about who had eaten the last chocolate chip cookie. Chuck said that Biff had done it; Biff said he was innocent; Rachel said that she had not been the one. Mrs. Collins knew that only one of her three children was a truther and that the other two were liars. So who ate the cookie?
12. difficulty: fairly easy
Last Saturday at the Sanchez family reunion, Nina had not seen her twin cousins Tyler and Tucker since childhood. When she ran into them all grown up, she recalled that, as kids Tucker never told the truth while Tyler was certainly a truther. "Tyler, Tucker...umm, which is which?" she asked. One of the cousins said, "The other one says he is Tucker." Which twin spoke?
At the Collins house, siblings Chuck, Biff and Rachel were being questioned about who had eaten the last chocolate chip cookie. Chuck said that Biff had done it; Biff said he was innocent; Rachel said that she had not been the one. Mrs. Collins knew that only one of her three children was a truther and that the other two were liars. So who ate the cookie?
Rachel.
If C is the truther, then there would be two people who had eaten the last cookie, R and B.
If R is the truther, there's a contradiction between B's and C's statements.
Therefore B is the truther. C's and R's statements are then false, and R is the guilty party.
Last Saturday at the Sanchez family reunion, Nina had not seen her twin cousins Tyler and Tucker since childhood. When she ran into them all grown up, she recalled that, as kids Tucker never told the truth while Tyler was certainly a truther. "Tyler, Tucker...umm, which is which?" she asked. One of the cousins said, "The other one says he is Tucker." Which twin spoke?
Tucker.
If Tyler spoke, he was telling the truth. But that would mean that Tucker, the liar, told the truth when he spoke. So Tucker lied about Tyler making the statement.
13. difficulty: medium
You have three bags, each containing two marbles. Bag A contains two red marbles, Bag B contains two blue marbles, and Bag C contains one red marble and one blue marble.
You pick a random bag and take out one marble.
It is a red marble.
What is the probability that the remaining marble from the same bag is also red?
14. difficulty: easy
You are being held captive. In a diabolical torture method, your captors starve you and then show you three baskets of food. One basket contains only nuts. One basket contains only berries. One basket contains both nuts and berries. The baskets are otherwise identical. They cover the baskets after showing you, and labels are secretly placed on them.
One says "nuts", one says "berries", and one says "nuts and berries". You are told that none of the baskets have been labeled correctly.
You can ask to see just one of the pieces of food from only one of the baskets without seeing what else is inside. If you can then ascertain which label properly goes to which basket, you can eat all the food. How can you do this?
Ask to see a fruit from the apples & oranges basket. Whichever fruit you see, move the proper "x only" label to it. Since all the baskets are improperly labeled, move the other "x only" label to the unlabeled basket. The remaining basket must be the real "apples and oranges" basket.
I'm inclined to say that it's 50/50 personally. Given that we have a red marble, we have either a blue one left or a red one, while the blue/blue bag is irrelevant.
This differs from the monty haul problem in that there is no case of probability on the first choice; GIVEN that one of the marbles in the bag we have is red, what is the chance of the other being red? The answer here would be 50%, as it's one of two possible bags and we chose randomly.
In the same manner as a coin flip, just because first marble removed was red has no effect on the likelyhood of the second marble being red. At the beginning of the test, you had a fixed chance of picking the bag with 2 red marbles, and THAT'S the important decision the question revolves around.
In the same manner as a coin flip, just because first marble removed was red has no effect on the likelyhood of the second marble being red. At the beginning of the test, you had a fixed chance of picking the bag with 2 red marbles, and THAT'S the important decision the question revolves around.
Answer: 1 in 3
13 - eh...
That implies that there's a 2/3rds chance of it being the R/U bag (since clearly, you didn't pick the UU bag).
All are equally likely. HOWEVER, 1, 2 and 3 have been shown not to be the case. Thus, it is 2/3. One of six things happened, and it's not 3 of them. So 33% chance of 4, 33% chance of 5, 33% chance of 6. No?
I am now posting puzzles for my facebook community. That is the reason my attendance has been spotty. I am giving away gift certificates as monthly prizes. You do not have to buy anything or join anything. There is nothing for sale. Just answer the puzzles and give me your opinions on them.
W and X must both be truthers, since they can't both be liars. Therefore Z is a liar and it's not Friday, and since Y is a truther, the day can't have an 's' in it. Monday is the only day remaining.
10. 1800.
Assume 1 is a liar:
-2 is a truther (from the second set of comments)
--The year isn't after 1742. (from 2's first comment)
But this means the year is before 1777, and 2 is telling the truth. This means 1's first statement is true, and he isn't a liar.
(Note that we also have the contradiction that the year isn't after 1742 and is 1850. Whatever floats your boat.)
1 is a truther:
-2 is a liar (again the second set)
--The year isn't 1850.
--The year is after 1742.
--Since 1 is a truther, the first part of his conditional 'the year is before 1777' must be false.
---This means that the year is 1777 or later.
Our only remaining option is 1800.
At the Collins house, siblings Chuck, Biff and Rachel were being questioned about who had eaten the last chocolate chip cookie. Chuck said that Biff had done it; Biff said he was innocent; Rachel said that she had not been the one. Mrs. Collins knew that only one of her three children was a truther and that the other two were liars. So who ate the cookie?
12. difficulty: fairly easy
Last Saturday at the Sanchez family reunion, Nina had not seen her twin cousins Tyler and Tucker since childhood. When she ran into them all grown up, she recalled that, as kids Tucker never told the truth while Tyler was certainly a truther. "Tyler, Tucker...umm, which is which?" she asked. One of the cousins said, "The other one says he is Tucker." Which twin spoke?
Rachel.
If R is the truther, there's a contradiction between B's and C's statements.
Therefore B is the truther. C's and R's statements are then false, and R is the guilty party.
Tucker.
If Tyler spoke, he was telling the truth. But that would mean that Tucker, the liar, told the truth when he spoke. So Tucker lied about Tyler making the statement.
I will have more puzzles essentially as soon I get a chance to look through my stash for good ones. I did not expect them to be solved so fast!!
You have three bags, each containing two marbles. Bag A contains two red marbles, Bag B contains two blue marbles, and Bag C contains one red marble and one blue marble.
You pick a random bag and take out one marble.
It is a red marble.
What is the probability that the remaining marble from the same bag is also red?
14. difficulty: easy
You are being held captive. In a diabolical torture method, your captors starve you and then show you three baskets of food. One basket contains only nuts. One basket contains only berries. One basket contains both nuts and berries. The baskets are otherwise identical. They cover the baskets after showing you, and labels are secretly placed on them.
One says "nuts", one says "berries", and one says "nuts and berries". You are told that none of the baskets have been labeled correctly.
You can ask to see just one of the pieces of food from only one of the baskets without seeing what else is inside. If you can then ascertain which label properly goes to which basket, you can eat all the food. How can you do this?
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This differs from the monty haul problem in that there is no case of probability on the first choice; GIVEN that one of the marbles in the bag we have is red, what is the chance of the other being red? The answer here would be 50%, as it's one of two possible bags and we chose randomly.
My blog.
Answer: 1 in 3
Note to self: Your mafia theories are usually wrong, so don't act on them.
13 - eh...
I believe what we have is...
One of these will happen:
1) Pick UU bag, pick U1
2) Pick UU bag, pick U2
3) Pick UR bag, pick U1
4) Pick UR bag, pick R2
5) Pick RR bag, pick R1
6) Pick RR bag, pick R2
All are equally likely. HOWEVER, 1, 2 and 3 have been shown not to be the case. Thus, it is 2/3. One of six things happened, and it's not 3 of them. So 33% chance of 4, 33% chance of 5, 33% chance of 6. No?
I am now posting puzzles for my facebook community. That is the reason my attendance has been spotty. I am giving away gift certificates as monthly prizes. You do not have to buy anything or join anything. There is nothing for sale. Just answer the puzzles and give me your opinions on them.
www.facebook.com/eimacs
Oops. I just realized that I have the link in my signature.