Puzzles/Brainteasers!

[C. D. Ward]

Solve this one, then post one of your own!

What do the following words have in common?

Store
Lease
Mark
Tire

[Em7add11]

They are both nouns and verbs?

[C. D. Ward]

They are both nouns and verbs?
That actually wasn't what I was thinking of, but it is true!

[Em7add11]

I've got it!

You leased something from Mark at the store and he was tired of you being there.

:teeth:

[truthman]

if you remove the first letter from each work, then they all make a new word

tore
ease
ark
ire

[C. D. Ward]

if you remove the first letter from each work, then they all make a new word

tore
ease
ark
ireActually, that's not what I was thinking of either, but that's a interesting coincidence!

I'd better edit my list to take care of that:

Vise
Lease
Mark
Tired

Okay, let's try again! Same question...

[Captain Ochre]

Actually, that's not what I was thinking of either, but that's a interesting coincidence!

I'd better edit my list to take care of that:

Vise
Lease
Mark
Tired

Okay, let's try again! Same question...

At the start I was going to say that they were all one syllable words--but "tired" is a bit dodgy for that solution.
:smile:

[C. D. Ward]

You're correct; that is a bit dodgy....

Any other takers? Want a hint?

[Captain Ochre]

You're correct; that is a bit dodgy....

Any other takers? Want a hint?

Yes, if only to let us know that it's a more arcane commonality than something like "all of the words begin with a capital letter".

:smile:

[TheAnalogman]

I'll take a hint for 200, Mr. Ward

meanolddogman

[im4him]

I get it haha i new that

[C. D. Ward]

Yes, if only to let us know that it's a more arcane commonality than something like "all of the words begin with a capital letter".:lol:

Okay, the common link these words share (and there are more that share it) is not related to grammar or syntax (or capitalization). It has more to do both with meanings and a common ability to manipulate...

Here's a few more words that fit the commonality; perhaps these will help?

Fuse
Spite
Cover
Late
Collect

[bar Jonah]

Actually, that's not what I was thinking of either, but that's a interesting coincidence!

I'd better edit my list to take care of that:

Vise
Lease
Mark
Tired

Okay, let's try again! Same question...
If you remove the first letter of each word, it does NOT create a new word?

:doh:

[C. D. Ward]

If you remove the first letter of each word, it does NOT create a new word?
:lmbo: :shifty:

Ma: We should be friends, after all, we've got a lot in common.
Friend: Like what?
Ma: Well, we both scrub floors....we're both swell lookers...and neither of us is Chinese!
Friend: Well, I'll say one thing for you...you've done your homework!

Johnny Dangerously

[Captain Ochre]

Ocky-Docky, I think I've got it.

Use a prefix such as "re" with each of the words and the result represents a distinct variance of meaning from the root (fuse, refuse is a good example).

Have I got it right?

[C. D. Ward]

Ocky-Docky, I think I've got it.

Use a prefix such as "re" with each of the words and the result represents a distinct variance of meaning from the root (fuse, refuse is a good example).

Have I got it right?
And we have a winner!! :bravo: :b_woot:

Okay, Cap'n, now it's your turn!

[Captain Ochre]

Uh, okay.
Here's one from long ago that doesn't seem too well-known (afaics):

You have ten stacks of ten coins before you.
One of the stacks is counterfeit.
Also before you is a rickety scale, capable of taking one weight measurement before breaking and becoming useless.

Counterfeit coins weigh one gram each, while the real ones weigh two grams each.

The challenge is to weigh one combination of coins in order to figure out which stack is the counterfeit one.

[C. D. Ward]

Also before you is a rickety scale, capable of taking one weight measurement before breaking and becoming useless.
I always heard that one as "you have a penny scale, but only one penny, so you can only take one weight measurement", but I suppose very few people know what a penny scale is anymore... :sad:

I'll recuse myself as I know the answer...:hehe:

[Benster]

All the words have at least four letters in them.

[TheAnalogman]

Take one coin from the first stack, take two from the second stack, three from the third, four from the fourth, and so on, till you're done with all 10 stacks. Weigh the 45 coins thus collected together and observe by how many grams the weighing result exceeds what 45 good coins would have yielded. If, for instance, you get a reading of 48, the 3rd stack of coins must be counterfeit. :b_woot:

[Captain Ochre]

Take one coin from the first stack, take two from the second stack, three from the third, four from the fourth, and so on, till you're done with all 10 stacks. Weigh the 45 coins thus collected together and observe by how many grams the weighing result exceeds what 45 good coins would have yielded. If, for instance, you get a reading of 48, the 3rd stack of coins must be counterfeit. :b_woot:

Bingo, analogman!
It's your turn to present a brainteaser or puzzle, afaict.

[TheAnalogman]

Chianlong, the Chinese Emperor, wanted to have a little fun with one of his councilors, a minister Liu. Holding up a precious vase he said to the minister: "I'm considering If I should give this vase to you as a gift. Two possibilities: I give it to you, and I don't give it to you. Which of the two ideas do you think I'm currently thinking about? If you guess correctly, the vase is yours."

With little hesitation, Minister Liu replied in such a way that he virtually secured the gift from the emperor. What did he say?

[C. D. Ward]

I don't like this answer, but it's the only one I can come up with that even part way works...

Minister Liu said, "Your majesty is thinking about not giving me the vase."

If he was correct, the emperor would have given him the vase. If he was incorrect, the emperor would still have been thinking about giving him the vase and so he would get it anyway.

I think the wording is such that his receipt of the vase isn't ensured, but it does say "virtually"...

How'd I do? :smile:

[TheAnalogman]

You did splendidly! Not only that, but you are also correct! :smile:

[C. D. Ward]

Okey-dokey! Here's another:

You walk into a room where three boxes of coins are labeled "gold", "silver", and "gold and silver". However, you're told that all three labels are wrong. If you can figure out the correct contents of each by drawing out one and only one coin, you can have all the silver and gold you can carry out of the room. How do you do it?

[TheAnalogman]

take one coin from the box labeled "gold and silver." Say that it's gold. You know that this must be the gold box, therefore the box labeled "silver" must contain mixed and the box labeled "gold" must actually be the silver coins.

[C. D. Ward]

That's it! Your turn again!

[C. D. Ward]

Hmmmm....this thread is dying! Must....rescue...

A very special forum is inhabited only by Knights and Knaves. Knights always tell the truth, and Knaves always lie. You meet two inhabitants: Ted and Zippy. Ted says, `Of I and Zippy, exactly one is a knight.' Zippy says that Ted is a knave.
So who is a knight and who is a knave?

[Em7add11]

Ted is a knight
Zippy is a knave

[C. D. Ward]

Very good! Your turn, now...

[Em7add11]

Hooray!

* goes to find a good brainteaser

Thank you for holding. Your post is very important to us. A rep will read your post as soon as one is available.

[luv1another]

umm Em are you going to post a brain teaser?

[C. D. Ward]

While we wait for Em to post one of his own, here's another to pass the time:

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet three inhabitants: Abe, Zoey and Zippy. Abe says, `At least one of the following is true: that Zippy is a knave or that I am a knight.' Zoey says, `Abe could claim that I am a knave.' Zippy claims, `Neither Abe nor Zoey are knights.'
So who is a knight and who is a knave?

[sylas]

While we wait for Em to post one of his own, here's another to pass the time:

A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet three inhabitants: Abe, Zoey and Zippy. Abe says, `At least one of the following is true: that Zippy is a knave or that I am a knight.' Zoey says, `Abe could claim that I am a knave.' Zippy claims, `Neither Abe nor Zoey are knights.'
So who is a knight and who is a knave?

Zippy is a Knight who speaks truely; both Abe and Zoe are knaves.

Now: this next puzzle has been described as the world's hardest puzzle.

A very special island is inhabited by knights, knaves, and jesters. Knights always speak the truth. Knaves always tell lies. Jesters say whatever they like.

You are at a fork in the road, with one branch leading to the pub, and the other to a bog. There are three individuals present. You know there is a knight, and a knave, and a jester; but you don't know which one is which. They do know each other, however. They all know also which road leads to the pub, and which to the bog, but you do not.

You need to get to the pub, and may ask each of the individuals one Yes/No question each; no more.

How can you pick questions to find out the way to the pub?

And just to make it a bit more difficult, they understand your questions, but answer in their own language, with the words "Da" and "Na". One of these means yes, and the other means no; but you don't know which is which.

Cheers -- Sylas

[C. D. Ward]

Sylas, you are truly evil. :grin: The eminent mathematician George Boolos called this the hardest logic puzzle *ever*.

Good luck, all!

[sylas]

Sylas, you are truly evil. :grin: The eminent mathematician George Boolos called this the hardest logic puzzle *ever*.

Good luck, all!

I think I screwed up. The hardest puzzle is to identify all three individuals using the three questions.

The puzzle as I have posed it (to find the pub) can (I think) be solved with two questions. Since I screwed up the puzzle, this stands as a new puzzle that is not so easily solved using google.

Cheers -- Sylas

[Benster]

Solve this one, then post one of your own!

What do the following words have in common?

Store
Lease
Mark
Tire
They all have at least one vowel and two consonants in them.

[Benster]

Solve this one, then post one of your own!

What do the following words have in common?

Store
Lease
Mark
Tire
They are all words of one syllable.

[Benster]

Solve this one, then post one of your own!

What do the following words have in common?

Store
Lease
Mark
Tire
They all begin with a letter that is between K and U.

[C. D. Ward]

:brood:

[Benster]

Solve this one, then post one of your own!

What do the following words have in common?

Store
Lease
Mark
Tire
If spelled backwards...they are all intelligible.

[Benster]

...sorry, I mean unintelligible.

[C. D. Ward]

:brood: :brood: :glare:

[Benster]

:brood:
Seriously, now:

They all contain either a vowel straddled by two consonants, or a consonant straddled by two vowels:

-ark
-ire-
-ase
-ise

That's got to be it!

[TheOneAndOnly]

Wow. Sylas' problem is hard, not least because I've heard it before and I know someone told me the answer but I can't remember what it was. I've tried for the last hour, with not much luck. And google's not being helpful either.

Here's one (i know it's not my turn):

Write out a ten digit number such that the first* digit of the number represents how many zeros are in the number, the second digit represents the number of 1s in the number and so on to the tenth digit, which represents the number of 9s in the number.


*By first digit I mean the furthest digit to the left.
e.g. in the number 4514 the first digit is 4, second 5...

[Benster]

I always heard that one as "you have a penny scale, but only one penny, so you can only take one weight measurement", but I suppose very few people know what a penny scale is anymore... :sad:

I'll recuse myself as I know the answer...:hehe:
You weigh one from the first stack, two from the second stack, etc.

If the scale is two heavy by one, then the first stack was counterfeit. Too heavy by two, then the second stack was, etc.

[C. D. Ward]

Write out a ten digit number such that the first* digit of the number represents how many zeros are in the number, the second digit represents the number of 1s in the number and so on to the tenth digit, which represents the number of 9s in the number.


*By first digit I mean the furthest digit to the left.
e.g. in the number 4514 the first digit is 4, second 5...
If I understood the directions correctly, I think 6,210,001,000 fits that bill...

[TheOneAndOnly]

If I understood the directions correctly, I think 6,210,001,000 fits that bill...

Yes. Have you heard it before or did you just work it out?

[C. D. Ward]

Yes. Have you heard it before or did you just work it out?
I had not heard that one before, but it wasn't too difficult to figure out. I knew right away that higher numbers most likely had to be zeroes (and thus zero a larger number). The trick was finding the "balance point" (how many zeroes?). After that, the other numbers pretty much dropped into place...

[Cyrus Johnson]

I had not heard that one before, but it wasn't too difficult to figure out. I knew right away that higher numbers most likely had to be zeroes (and thus zero a larger number). The trick was finding the "balance point" (how many zeroes?). After that, the other numbers pretty much dropped into place...

Since there's no solution yet to Sylas' 'which way to the pub' problem, and believe me haven't any to offer, how about another easier one in a socceresque theme?

Three cards are placed unseen in a sack. One card is yellow on both sides, one card is red on both sides, and the third card is yellow on one side and red on the other. Otherwise the cards are identicle. Suppose a card is drawn from the sack at random and placed on a table.

The side showing up is red.

What is the probability that the other side of this card is also red?

[TheOneAndOnly]

P(A|B) = P(A and B)/P(B)
So the prob the second side is red given the first side is red is 1/3 divided by 1/2 which is 2/3.

[sylas]

Since there's no solution yet to Sylas' 'which way to the pub' problem...

I mixed up two problems in my own phrasing, with the end result that my puzzle is probably genuinely new.

I've got a nice solution with simple questions in English; the added complexity of languages makes the solution less elegant.

So my puzzle is as follows:

A knight, a knave and a jester are all sitting at a fork in the road. You don't know which is which, but they all do; and they also know which road leads to the pub. The knave always tells lies, and the knight always speaks truth. The jester just says what he likes. Using two yes/no questions, each one to a single one of these individuals, identify which fork of the road goes to the pub.

I'll give my solution in due course.

Cheers -- Sylas

Added in edit. For powerful hints, see the article: The Hardest Logic Puzzle Ever (http://people.ucsc.edu/~jburke/three_gods.pdf) by George Boolos. (Thanks for the name C.D. It let me find this paper again.) Gives the essential method.

[Cyrus Johnson]

P(A|B) = P(A and B)/P(B)
So the prob the second side is red given the first side is red is 1/3 divided by 1/2 which is 2/3.

Yes! Nice work.

That was apparently easier than I thought.

[sylas]

This article gives the solution to my knight/knave/jester puzzle. (Another puzzle might be to read the solution.)

Solution:

Point to one individual and ask a different individual: Could you call this person a jester?

If the answer is no, then turn to that individual you pointed out. If the answer is yes then turn to the third individual.

Point to one fork, and ask the person you have now turned to: Could both of the others identify this as the road to the pub?

If the answer is no, then go that way. Otherwise go the other way.

Why it works:


The objective of the first question is to identify anyone who is not a jester. If you asked the jester, then by elimination asking someone else is asking a knight or a knave. If you asked the knight, then they simply answer yes when you point to the jester, and no if you do not. If you asked the knave, then if you are pointing to the jester the knave could not identify that person as the jester. But since the knave answers untruthfully, then they will say "yes" when you do point to the jester, and "no" when you do not.

The second question is constructed to ensure knights and knaves give the same answers. If you ask a knight whether both the other two can identify this as the pub road, then because one of the others is a knave they will answer "no" for the pub road, and "yes" for the road that does not go to the pub. If you ask a knave, then because one of the others is a knight, they will answer "no" for the pub road, because actually both the others could identify the pub road, and the knave lies about this. They will answer "yes" for the non-pub road, because actually the others could not both confirm this as the pub road, and again the knave has to lie about it.


Cheers -- Sylas

[Tickle Me Goody]

I think I screwed up. The hardest puzzle is to identify all three individuals using the three questions.

The puzzle as I have posed it (to find the pub) can (I think) be solved with two questions. Since I screwed up the puzzle, this stands as a new puzzle that is not so easily solved using google.

Cheers -- Sylas
I believe that these types of problems can always be answered without the IFF condition as follows:

1.) It is possibel to pharse a question such that one always gets a truthful answer (by using the phrase "if someone were to ask you...") whether the individual lies or not.

2.) It is possible to phase a question such that the actual meanings of the responses are irrelevant but just that only a binary response is allowed.

Example:

To A: If someone were to ask you to say "Da" if B is a jester (and "Ja" if he is not) what would you say?

To B: If someone were to ask you to say "Da" if A is a jester (and "Ja" if he is not) what would you say?

We now know who the jester is:

Da, Da: Impossible

Da, Ja: B is the jseter

Ja, Da: A is the jester

Ja, Ja: C is the jester

Say that we know that that B is not the jester.

To C: If someone were to ask you to say "Da" if B is a knight (and "Ja" if he is not) what would you say?


Is there a flaw in this approach?

Goody