Solve Enjoyable Enigmas with Mr.E's Challenge

[zoobyshoe]

DOH!

Spoiler

Homer inspires me...3*5=15...never thought about the special cases of letters aka vowels I even tried adding subtracting multiplying no. of letters and no. of syllables...

Spoiler

But Jim has one vowel and Neal has two, but both are 5. So, it's not vowels.

 

[Enigman]

I should be banned for that mistake...

 

[zoobyshoe]

I never completely confirmed it, but Collinsmark gave the answer the book asserts as right: 85%. This is the average of the two separate probabilities, 80% and 90%.

 

[Enigman]

I should be banned twice...I still don't get it...enough for now...:zzz:
Mr.E out.

 

[consciousness]

If Susan is 10, Arabella is 20, and Jim and Neal are both 5, but Richard is 10, how much is Jennifer by the same logic?

Spoiler

Does the answer depend on the number of maximum repeating alphabets? Jennifer is 10 this way.

 

[Enigman]

Spoiler

Does the answer depend on the number of maximum repeating alphabets? Jennifer is 10 this way.

Spoiler

Actually, she's 20(2e,2n)...but if that were the case Arabella shouldn't be 20 she should be either 25(total no. of repeating letters) or 10(no of. repeating type of letters)

But I don't know, I seem to have my lost my wits recently...

 

[lisab]

Spoiler

Actually, she's 20(2e,2n)...but if that were the case Arabella shouldn't be 20 she should be either 25(total no. of repeating letters) or 10(no of. repeating type of letters)

But I don't know, I seem to have my lost my wits recently...

Spoiler

No, Jenifer would be 15. It's # of syllables X 5. Syllables is 15, too .

 

[Enigman]

Spoiler

No, Jenifer would be 15. It's # of syllables X 5. Syllables is 15, too .

Milady, you just saved me from another sleepless night...
---------------------------------------------------------------
I can swear that syllables didn't add up but it was 3:00 am then...
P.S. feel free to ban me, I deserve it...2 mistakes in a row...ban me twice...

 

[Enigman]

Next one:
There's a bowl of water and some pepper is floating in it. Assume that the pepper is in an approximately uniform distribution.
Using anyone household materials you need to move all the pepper in the centre to the sides of the bowl. And do it quickly.

 

[Enigman]

mmm...two more answers occurred to me...
(#609)

 

[collinsmark]

Next one:
There's a bowl of water and some pepper is floating in it. Assume that the pepper is in an approximately uniform distribution.
Using anyone household materials you need to move all the pepper in the centre to the sides of the bowl. And do it quickly.

I know the answer to this one so I'll bow out.

(I've known about this one since childhood. I remember it because it was originally presented to me as part of a rather off-color joke. I was young enough that I hadn't been exposed to many off-colored jokes before, and I didn't comprehend the humor. But I did enjoy the science of the thing though, regardless of its presentation.)

 

[Enigman]

I know the answer to this one so I'll bow out.

(I've known about this one since childhood. I remember it because it was originally presented to me as part of a rather off-color joke. I was young enough that I hadn't been exposed to many off-colored jokes before, and I didn't comprehend the humor. But I did enjoy the science of the thing though, regardless of its presentation.)

Yes, its one of my favourites too.(right after burning an emptied tea bag*...)
You can use it to 'power' small paper boats too...
I miss being a kid...

*https://www.youtube.com/watch?v=SIa4WPRTlf8

 

[zoobyshoe]

Spoiler

No, Jenifer would be 15. It's # of syllables X 5. Syllables is 15, too .

Spoiler

This is CORRECT! Each syllable in a name is worth 5. I posted a riddle earlier where each letter in a word was worth 1.5 dollars. I think that primed people to think in terms of number of letters. When that didn't pan out, they tried number of consonants and vowels. No one seems to have authentically tried number of syllables.

 

[Enigman]

I did...

 

[zoobyshoe]

I did...

It happens. Once I added 40 + 40 + 40 + 40 to 80. My brain just randomly goes on break sometimes.

 

[lisab]

Next one:
There's a bowl of water and some pepper is floating in it. Assume that the pepper is in an approximately uniform distribution.
Using anyone household materials you need to move all the pepper in the centre to the sides of the bowl. And do it quickly.

My closest experience with this is fleas. We were infested once, they were everywhere! I learned to catch them and put them in a glass of water. But they would float on the surface forever, and sometimes even make their way back out!

So I discovered the trick: one drop of dish washing detergent.

Pretty sure it would work for pepper, too. Ah jeez I have a science degree, I should experiment...<runs off to kitchen>

 

[drizzle]

Ginger or citrus zest would do it, or a toothpaste... I have experience you see.

 

[lisab]

Ginger or citrus zest would do it, or a toothpaste... I have experience you see.

Oddly enough I have neither ginger nor a lemon at this time! I'll have to check out toothpaste later. Detergent definitely works, though.

 

[consciousness]

Another possible answer-

Spoiler

Disturb the surface to create a small hole in the pepper distribution near the center of the bowl. Then put oil there. As the oil spreads the pepper is collected at the water-oil interface. Eventually it will all be at the side,

 

[drizzle]

Your method is probably faster, consciousness.

 

[Enigman]

LisaB, conciousness are both correct. Gad's toothpaste works too. Don't know about lemon...don't have any...

 

[zoobyshoe]

Wow, that's a neat magic trick! I'm surprised how fast the pepper spreads.

 

[consciousness]

That must be a very strong detergent!

Next one-

There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Also, there are no reflective surfaces on the whole island. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not say anything about them. Life goes on, with brown-eyed monks and red-eyed monks living happily together in peace, and no one ever committing suicide. Then one day a tourist visits the island monastery, and, not knowing that he's not supposed to talk about eyes, he states the observation "At least one of you has red eyes." Having acquired this new information, something dramatic happens among the monks. What happens?

Note-Ignore the fact that they can see their reflection in water.

My addition to the problem-Find the number of days after which nothing happens.(If there are m,n red and brown eyed monks respectively.

 

[lendav_rott]

Spoiler

What new information would the tourist's comment bring to the table? He says atleast one of the monks has red-eyes, but the monks can see so they know if it is true or not without the tourist saying it. Also they are all under a vow of silence, nobody will ever know their own eye-colour so nobody can commit suicide. Nothing should happen among the monks.

 

[Enigman]

Only thing I can think of:

Spoiler

Assuming each and every monk can see all other monks and tourist has seen every monk and monks cannot communicate at all.
Something dramatic happens only -
a)if there's only one monk with red eyes- and he commits suicide...
b)if there are no monks with red eyes(tourist lies)- everyone commits suicide...

 

[consciousness]

Think harder.

 

[lendav_rott]

Spoiler

Ok, if there were 2 monks and the tourist says "one of you has red eyes" - that still means nothing. Who is to say if the tourist even speaks the truth? Maybe both the monks have red/brown eyes. There are so many loose ends. One, for example, will the monks commit suicide based on the Fact that they Know they have red eyes or based on an assumption? Any suicide committed would be solely subjective, therefore there is no 1 concrete solution to this riddle

 

[consciousness]

Spoiler

Ok, if there were 2 monks and the tourist says "one of you has red eyes" - that still means nothing. Who is to say if the tourist even speaks the truth? Maybe both the monks have red/brown eyes. There are so many loose ends. One, for example, will the monks commit suicide based on the Fact that they Know they have red eyes or based on an assumption? Any suicide committed would be solely subjective, therefore there is no 1 concrete solution to this riddle

I didn't think that I needed to write this - the monks will believe the tourist as long as when he is obviously lying. See Enigman's post. Its not the answer but tells about how to think of the problem.

The debate about the tourist entering information into the system is an interesting one but engaging in it now would spoil the riddle.

 

[zoobyshoe]

Spoiler

The monks rigidly obey their vow of silence, so we can assume they would obey the injunction to commit suicide if they thought they had red eyes. What's been preventing that is that no one has any way to know if they have red eyes.

Minimum number of monks is two, since they're referred to with the plural form. Armed with the visitor's information the one who has red eyes would see the other has brown and would commit suicide.

For larger numbers of monks: in any situation where a monk sees that all other monks have brown eyes, he will commit suicide. If he sees any others with red eyes, he's off the hook; the "at least one" red eyed monk has been accounted for.

 

[collinsmark]

That must be a very strong detergent!

Next one-

There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes are cursed, and are supposed to commit suicide at midnight. However, no one ever talks about what color eyes they have, because the monks have a vow of silence. Also, there are no reflective surfaces on the whole island. Thus, no one knows their own eye color; they can only see the eye colors of other people, and not say anything about them. Life goes on, with brown-eyed monks and red-eyed monks living happily together in peace, and no one ever committing suicide. Then one day a tourist visits the island monastery, and, not knowing that he's not supposed to talk about eyes, he states the observation "At least one of you has red eyes." Having acquired this new information, something dramatic happens among the monks. What happens?

Note-Ignore the fact that they can see their reflection in water.

My addition to the problem-Find the number of days after which nothing happens.(If there are m,n red and brown eyed monks respectively.

Only thing I can think of:

Spoiler

Assuming each and every monk can see all other monks and tourist has seen every monk and monks cannot communicate at all.
Something dramatic happens only -
a)if there's only one monk with red eyes- and he commits suicide...
b)if there are no monks with red eyes(tourist lies)- everyone commits suicide...

Spoiler

I think Enigman is on the right track. But I'll put my own spin on it.
One of two things happens:
a) The one monk with the red eyes gouges one of his eyes out. The then washes the blood off, examines it with his remaining eye, realizes he has red eyes, and proceeds to kill himself that night at midnight.
b) There are no monks with red eyes, but they are not 100% sure if the tourist is telling the truth or lying. The original wording said that something dramatic happens so we can assume that at least one monk will attempt to gouge one of his eyes out (that's the dramatic part). The rest of the monks, seeing a brown eyed monk gouging one of his eyes out, realize the tourist is lying. After examining the eye, after washing the blood off, even the now one-eyed monk realizes the tourist is lying.

[Edit: I intentionally didn't include the situation where there are several red eyed monks because then nothing dramatic would happen in that case.]

 

[zoobyshoe]

Spoiler

b) There are no monks with red eyes, but they are not 100% sure if the tourist is telling the truth or lying. The original wording said that something dramatic happens so we can assume that at least one monk will attempt to gouge one of his eyes out (that's the dramatic part). The rest of the monks, seeing a brown eyed monk gouging one of his eyes out, realize the tourist is lying. After examining the eye, after washing the blood off, even the now one-eyed monk realizes the tourist is lying.

Spoiler

That's pretty dramatic. That audience won't believe it though, unless we write in a stipulation that they take their vow of silence so seriously, they'd rather lose an eye than break it.

 

[collinsmark]

Spoiler

I think Enigman is on the right track. But I'll put my own spin on it.
One of two things happens:
a) The one monk with the red eyes gouges one of his eyes out. The then washes the blood off, examines it with his remaining eye, realizes he has red eyes, and proceeds to kill himself that night at midnight.
b) There are no monks with red eyes, but they are not 100% sure if the tourist is telling the truth or lying. The original wording said that something dramatic happens so we can assume that at least one monk will attempt to gouge one of his eyes out (that's the dramatic part). The rest of the monks, seeing a brown eyed monk gouging one of his eyes out, realize the tourist is lying. After examining the eye, after washing the blood off, even the now one-eyed monk realizes the tourist is lying.

[Edit: I intentionally didn't include the situation where there are several red eyed monks because then nothing dramatic would happen in that case.]

Spoiler

Hmmm. Thinking about this a little more, things might actually get a little interesting if there are several red-eyed monks.

Suppose that there are exactly two red-eyed monks. Nothing would happen on the first day (and first midnight) because even the red-eyed monks know that there is at least one red-eyed monk.

However, each red-eyed monk would expect the other to gouge his eyes out and commit suicide if there were only 1 red eyed monk. But on the following day, neither monk has killed himself. Because the other red eyed monk is still alive, each red eyed monk can logically deduce to himself, "that red eyed monk is able to see the red eyes of another monk (otherwise he would have killed himself by now), and since I only see the red eyes of the one monk, the other monk must be me!" So on the second day, each of the red eyed monks gouge their own respective eyes out* and commit suicide at the second midnight.

Similarly if there are exactly three red eyed monks they would gouge an eye out on the third day and kill themselves on the third midnight and so on.

So in conclusion, if there are n red eyed monks they would gouge their eye out on the nth day, and kill themselves on the nth midnight.

*(They gouge their own eye out for good measure.)

 

[consciousness]

Collinsmark, you have pretty much got it. The way I thought about this one was that the monks believe the tourist, so there is no eye gouging.

There is a nice way to organise your solution using

Spoiler

Mathematical Induction

.

 

[collinsmark]

Here's sort of a mathy one that doesn't involve gouging out sensory organs or committing suicide. Instead, it's only about trains. Nice, relaxing trains.

A man retires from his job and moves to the countryside. He's sick of the hustle-and-bustle of the city and decides never to even wear a wristwatch any more or even keep clocks in his house.

He's always enjoyed trains (as in railroad) though, and happens to live next to a railroad track. Each day, at a completely random time, he walks out to tracks and waits for a train. After watching a train go by he goes back home for the rest of the day and records whether the train was a yellow train or a red train.

After months and months of data, he notices that for every red train he has seen, he has seen about 5 yellow trains. (i.e. 5 yellow trains to every 1 red train.)

One day he goes into the town to get groceries and mentions this to the shopkeeper, who knows quite a lot about local trains and train schedules. The shopkeeper informs him that the trains are on a very tight schedule and the red train passes on the tracks near his house on the hour every hour (12:00, 1:00, 2:00, 3:00, etc.). And to the man's surprise, the shopkeeper also informs him that the red and yellow trains alternate, one after the other, also at a set schedule, and there are an equal number of red trains as yellow trains that pass on the tracks near his house. And those are the only trains that ever use those tracks. [Edit: by all that I mean the yellow trains are also on a fixed schedule. And for any given hour of the day, two trains will pass: one red and one yellow.]

How can this be? Why did he see so many more yellow trains than red trains?

Stipulations:
(a) The red trains and the yellow trains are all of equal size/length, and that size is rather short: just a couple of cars or so.
(b) Although trains are involved, this enigma has nothing to do with special relativity or the Doppler effect. They are just normal trains (albeit short ones) moving at normal train speeds.

 

[zoobyshoe]

You say the trains will "pass". Does this mean red trains only go in one direction and yellow trains in the opposite direction?

 

[collinsmark]

You say the trains will "pass". Does this mean red trains only go in one direction and yellow trains in the opposite direction?

Hmm. Either way will work.

But when I said "pass" I mean pass by his house. The trains do not pass by his house and each other at the same time (if they even pass each other at all -- all trains can all be going in the same direction at the same speed for this). [They can also travel in different directions but it's not necessary.]

So whichever direction, from the location of his house, there is nor more than one train going by at any point in time.

 

[zoobyshoe]

Hmm. Either way will work.

But when I said "pass" I mean pass by his house. The trains do not pass by his house and each other at the same time (if they even pass each other at all -- all trains can all be going in the same direction at the same speed for this). [They can also travel in different directions but it's not necessary.]

So whichever direction, from the location of his house, there is nor more than one train going by at any point in time.

Thanks.

The red trains are on the hour every hour. The yellow trains are exactly one per hour, but we don't know if it's a quarter past the hour, a quarter before, on the half hour, or what, right?

 

[collinsmark]

Thanks.

The red trains are on the hour every hour. The yellow trains are exactly one per hour, but we don't know if it's a quarter past the hour, a quarter before, on the half hour, or what, right?

Yes, that's the right idea! Think about this one some more, the answer will arrive.

Spoiler

[Hint: Remember, the man comes to wait for a train (any train) at a completely random time, once per day. ]

 

[zoobyshoe]

Spoiler

Well, I would suppose he's actually being prompted by the passing of a red train without realizing it. The yellow trains probably follow the red trains by a small amount of time. He hears a train and subliminally is prompted to go out and wait.

Once in a while he doesn't make it out in time to see a yellow train and happens to catch the next red one, then goes home.

 

[collinsmark]

Spoiler

Well, I would suppose he's actually being prompted by the passing of a red train without realizing it. The yellow trains probably follow the red trains by a small amount of time. He hears a train and subliminally is prompted to go out and wait.

Once in a while he doesn't make it out in time to see a yellow train and happens to catch the next red one, then goes home.

Spoiler

Not quite. I thought you almost had it there for a second, but then you mentioned the prompting part. He's not prompted by anything (subliminally or otherwise). He really goes out to wait at a random time each day.

 

[collinsmark]

Spoiler

Well, I would suppose he's actually being prompted by the passing of a red train without realizing it. The yellow trains probably follow the red trains by a small amount of time. He hears a train and subliminally is prompted to go out and wait.

Once in a while he doesn't make it out in time to see a yellow train and happens to catch the next red one, then goes home.

Spoiler

Hmmm. I might just give it to you. But just to solidify everything, let me ask this first: at what time of the hour do the yellow trains pass by his house?

 

[zoobyshoe]

Spoiler

Hmmm. I might just give it to you. But just to solidify everything, let me ask this first: at what time of the hour do the yellow trains pass by his house?

Spoiler

I don't see there's any way to determine the exact time, but it would be more likely to be shortly after the red trains pass, assuming it doesn't take him long to get to the tracks.

 

[lisab]

Spoiler

this is the quietest thread on the forum, i think

 

[zoobyshoe]

Spoiler

I suddenly realized where you might be going: if the yellow train always precedes the red by a few minutes or so, then it is more likely that's the one he'll see on authentically random excursions. If they both go past within 10 minutes of each other, with the yellow always first, then there is a 50 minute period during which his decision to go out will feel "random," but will, 5 times out of 6, be concluded by seeing a yellow train. He'll see it, then leave before the red one goes by. Once out of 6 times, though, he'll get out there just after the yellow train has passed by and he'll see the red train.

 

[consciousness]

Spoiler

The yellow trains arrive 10 minutes before the red trains.

 

[collinsmark]

Spoiler

I suddenly realized where you might be going: if the yellow train always precedes the red by a few minutes or so, then it is more likely that's the one he'll see on authentically random excursions. If they both go past within 10 minutes of each other, with the yellow always first, then there is a 50 minute period during which his decision to go out will feel "random," but will, 5 times out of 6, be concluded by seeing a yellow train. He'll see it, then leave before the red one goes by. Once out of 6 times, though, he'll get out there just after the yellow train has passed by and he'll see the red train.

Spoiler

The yellow trains arrive 10 minutes before the red trains.

Yes, these are both correct answers.

 

[zoobyshoe]

Yes, these are both correct answers.

That was an interesting situation, where two equal things looked to be quite unequal.

 

[zoobyshoe]

It was time to send the kids to camp, and Sally and Jim were shopping for supplies. They spent half of the money they had plus $4 on socks for the kids; half of what was then left plus $3 on name tapes; and half of what was then left plus $2 on a small wallet for each child. They found themselves with $3 left over. How much did they start with?

FWIW: The book says only 70% of Mensa members who tackled this one got it right. I don't know why. It didn't seem to be that tricky to me.

 

[zoobyshoe]

Here's the kind Gad and Enigman like:

My first is in sugar but not in tea
My second in swim but not in sea
My third in apple and also pear
My fourth in ring and also hare
My last in ten but not in herd
My whole a very complimentary word.

 

[drizzle]

is there 'o' in the word?