Solve Enjoyable Enigmas with Mr.E's Challenge

[Enigman]

EDIT-*crossed posts with collinsmark but hopefully between two of us we could clear it up better.
*
Ok, so let's begin with the variables:

• a-no. of pennies b-no. of half-dollars c-no. of quarters d- no. of dimes e-no. of nickels
• the equations that have to hold are:

1. a+b+c+d+e=50
2. 0.01a+0.5b+0.25c+0.1d+0.05e=1

• But it is a general rule of math that to get unique values for all variables we need at least as many equations as there are variables- otherwise there are infinite solutions.
• But we have the constraint that a.b.c.d.e are number of coins so they are whole numbers less than 50(total no. of coins)
• After this we see that as lendav_rott said no. of pennies has to be non-zero otherwise we won't get anything near 50 coins.
• then the no. of pennies has to be a multiple of 5 with units place 5 or 0 as otherwise we have no chance of getting $1 as sum- because all other values of coins in terms of pennies are multiples of 5.
• After that its trial and error. 45 pennies and 40 pennies check out.
• When we reach 35 we see that the no. of nickels can't cover it from then on to make 50. (nickels being the least valued after a penny)
• So we can conclude that 45 and 40 pennies are the only case possible.
• Assuming equal probability for both cases 1/2*45/50+1/2*40/50=0.85

Hope that clears things up a bit.

 

[zoobyshoe]

EDIT-*crossed posts with collinsmark but hopefully between two of us we could clear it up better.
*
Ok, so let's begin with the variables:
a-no. of pennies b-no. of half-dollars c-no. of quarters d- no. of dimes e-no. of nickels
the equations that have to hold are:
a+b+c+d+e=50
0.01a+0.5b+0.25c+0.1d+0.05e=1
But it is a general rule of math that to get unique values for all variables we need at least as many equations as there are variables otherwise there are infinite solutions.
But we have the constraint that a.b.c.d.e are number of coins so they are whole numbers less than 50(total no. of coins)
After this we see that as lendav_rott said no. of pennies has to be non-zero otherwise we won't get anything near 50 coins.
then the no. of pennies has to be a multiple of 5 with units place 5 or 0 as otherwise we have no chance of getting $1 as sum- because all other values of coins in terms of pennies are multiples of 5.
After that its trial and error. 45 pennies and 40 pennies check out.
When we reach 35 we see that the no. of nickels can't cover it from then on to make 50. (nickels being the least valued after a penny)
So we can conclude that 45 and 40 pennies are the only case possible.
Assuming equal probability for both cases 1/2*45/50+1/2*40/50=0.85
Hope that clears things up a bit.

I will cogitate on this. Thanks.

 

[zoobyshoe]

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?

 

[Enigman]

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...

 

[BobG]

Spoiler

Replacing a penny increases your total amount of money by 4 cents.

50 pennies is 50 cents away from a $1, which isn't a number divisible by 4, so there has to be some dimes. Replacing 1 penny with 1 dime gets me to 59 cents, 41 cents obviously isn't divisible by 4, so...

Replacing 2 pennies with 2 dimes gets me 68 cents. 32 cents is divisible by 4, so I replace 8 more pennies with nickles to get $1.

No odd number of dimes is going to help me. Replacing 4 pennies with dimes gets me to 86 cents. 14 isn't divisible by 4.

I can go to 6, but that puts me over $1.00 before I even start with the nickles.

Replacing a penny with a quarter gets me to 74 cents. 26 cents isn't divisible by 4.

Going with a quarter and 1 dime gets me to an odd number.

Going with a quarter and 2 dimes gets me to 92 cents. Replacing two more of the pennies gets me to $1.00.

Going with a quarter and 4 dimes is over $1. With half a dollar I'm already at 99 cents.

So there's two solutions: 2 dimes, 8 nickles, and 40 pennies. 1 quarter, 2 dimes, 2 nickles, and 45 pennies.

Edit: Actually, I forgot about a solution with dimes and pennies, and no nickles. But since replacing a penny with a dime increases the amount by 9 and 50 isn't divisible by 9, I got lucky. There are no solutions with just dimes and pennies.

And likewise, there are no solutions with quarters and pennies only. And since replacing 1 penny with a quarter gets me to 74 and 26 isn't divisible by 9, there are no solutions with quarters, dimes, and pennies only.

 

[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.]