Pretty sure the answer is just "40 minutes" and it is a question to make someone think about what they are doing rather than automatically solve every task.
IIRC the speed of the 9th symphony is somewhat controversial because what markings we have on original sheetmusic are significantly faster than it's normally played.
Symphony music in general is going to vary a decent bit depending on what bpm(s) the conductor is choosing.
Any decent conductor is going to to vary the beat based on how long it takes for sound to fill the venue in question. Beethoven's choices for the music halls in Vienna might have made sense then, but not so much today.
One of the things that's always annoyed the conductors that I've worked with is that we always ignore the dynamics in his music. Beethoven's markings are expressive, subtle. And we always play his stuff louder than indicated.
I'd like to think it's a really clever question about making people verify what's written before them, rather than taking everything at face value and absolute fact.
This is similar to something I assumed right before I had a long argument with a high school physics teacher. We ended up agreeing that he just didn't really care.
For anyone who hasn't read The Mythical Man-Month, it is a timeless, compelling, relevant book on software engineering and project management. It is also accessible to non-technical audiences with lessons that apply across much of modern workforces.
Yes, which is why I phrased my statement as "Well, ... could..." to indicate an alternative perspective. This was to illustrate that sometimes pithy reductive quips can be based on overly reductive assumptions. Maybe it is the case that a single baby is all that's required, but maybe the author misunderstood the goal.
In this fictional scenario of the author's creation? That just demonstrates the converse - that sometimes simple ideas will be deliberately misinterpreted in a convoluted way, to prove someone else's point.
With something like a baby, people know what's going on and what's meant. That's why it's the example. But when it comes to esoteric things, playing word games just confuses the issue and will lead to a manager thinking that indeed 9 woman can give you a baby in 1 month (I'm not jumping through your word games, you know what's meant).
Making assumptions about what's meant, and expecting people to make assumptions about what you mean, is how problems happen. Thorough communication is the cornerstone of understanding.
Playing games with "it could be interpreted this way if I tried really really hard" and frankly being intentionally obtuse is how problems happen. Don't intentionally contribute to miscommunication. You can play games online, in real life this doesn't help anyone.
Why couldn't 9 women deliver a baby in one month? That's perfectly reasonable. Put the baby in a vehicle. Drive. Maybe stop at some hotels or just sleep in the vehicle with all 9 women. Then eventually you reach your destination in 1 month. Deliver baby. Profit.
My kid showed me a test question from a junior high math test about construction a building in 12 months with x number of workers, how many workers do they need to hire if they want it done in 6 months.
So I guess if you answer that question "wrong" youd be smart, and if you answer it right, management. Even a junior high student mocked it...
Well, if T is total time to build, D is the time that can be distributed equally among any number of workers, and C is constant, indivisible time extra time that goes along with construction, and X is the number of workers, then:
T - C = D / X
so, since T is 12 and 6 is half of 12, then:
T/2 - C = D/X * 1/2
or
T/2 - C = D/2X where X > 0, C = 0, T=12, and D = (T - C) / X
which is both the answer it's looking for (twice as many workers) and the correct answer (it depends on at least two things we don't know), while assuming what they're assuming, which is C = 0
(Stupid ass junior high math problems piss me off, junior high is a traumatic experience)
Well, arguably still "incorrect" in real world terms since it fails to have an adjustment for divisibility of D as a function of how many people. If theoretically a task is "perfectly divisible" at two people and halves the time, it will not be the case that a million people will cause it to happen in one millionth of the time. Improvement by expressly pointing out "C" and declaring your assumption of zero for math to work. Also assumption than for any increment of X, the time impact is equal.
In math this is pedantic, but it sure impact project planning in very disastrous ways, and business people love to assume C is zero, any change to X is linear and with linear impact, and make embarrassingly bad calls as a result.
yup, but that answer was based entirely on the assumptions present in the question. D is all divisible work, and C is everything else, because that's literally all you can assume to make the math work. D has to therefore be 12 months worth of divisible work minus C. C could very well be 12 months of work, meaning D is zero and adding more workers won't matter.
I feel like a lot of the puzzles in Professor Layton games are like this. Any time you find yourself starting some complex algebra or multiplication, you need to consider rereading the problem and seeing if you just need to pick a number that’s there.
For example: A bus can travel 100 miles on a full tank with its full passenger load of 80 people. If everyone gets off the bus, then how far can it travel?
::: spoiler The answer
0 miles. With everyone off, there’s no one to drive it.
:::
Snopes says this is "undetermined" (also that CDs hold 74 minutes). Honesty pleasently surprised by how plausible it is from the given evidence though, I was expecting this to turn out to be definitively a myth.
I did orchestra as student, and there's so much you get out of watching the conductor, way more than the downbeat, and a good conductor, orchestra relationship can get to the point subtle nuances effect how you play, and I just imagine a guy trying to conduct and hold his cheeks closed, and the whole rushed performance sounding absurd with unintentional volume and speed changing abruptly all over the place.
It is. The original worksheet it's cropped from says "beware, one of these is a trick question!", but obviously that was cropped out because someone really wanted to create an opportunity to feel superior to someone.
Reminds me of an animator saying ''If a pregnant woman takes nine months to have a baby, can four women have a baby in two and a half months?''
The point is, somethings can't be done faster through simple numbers. Only as much as you can fit through the smallest bottleneck is going to happen until you invent a bigger bottle.
Most speedrunners know about the glitch in Beethoven's 9th where if you have the entire brass section make a quarter turn to the left at just the right moment of the open fifths the whole symphony freezes for a second and then drops you straight into the Ode to Joy.
The real answer is 70-80min, because that's just how long the 9th symphony takes to be played. And they better add a chorus as well, otherwise the 4th movement won't be as good as it normally is
Let’s say you put like 1000 violinists all in a big, long row. Then, have the first violinist play a note, then the second plays the very same note, then the third, and so on. Let’s say you could also time it so that at the very moment the sound wave from one violinist hits the next is when that one plays the note. Brrrrrrump! All the way across. Let’s also say you could time it perfectly so that the waves don’t cancel each other out. What would happen?
I think eventually you reach a point where previously played notes would lose all of their energy, meaning there's probably an upper limit on how loud it would get for an observer at the end. Something something Doppler effect.
Not the Doppler effect, as that only applies to moving objects, but instead the inverse square law, where the energy of the sound wave decreases by the square of the distance from the origin, since it spreads in a sphere with the energy being spread across the surface of the sphere, resulting in a very quick dropoff in the loudness.
As I was going to St. Ives I met a man with seven wives. Each wife had 7 sacks, each sack had 7 cats, each cat had 7 kits. Kits, cats, sacks, wives; how many were going to St. Ives?
This is a stupid riddle, because maybe they were walking in the same direction. I'd expect the guy with all the wives and cats to be making slower progress, you know?
Well, the answer is "at least 1". We don't know the destination of the polygamist or whether there were other travellers with less remarkable entourages.
St. Ives is a popular tourist destination, but stupidly remote and takes a long time to reach. It's likely that there are several people travelling to St. Ives at any given moment.
We need a player for every note in the score(tied notes can be played by a single musician). On the conductor's downstroke everyone plays their note. Every note of the 9th played simultaneously. I want to hear this, but I don't think that my poor old computer would function if I opened that many individual instruments in Reason.
Just put the orchestra on a spaceship approaching light speed, and you can take even less time (relatively experienced by an off-spaceship audience.) If you still want the shockwave, you can use an Alcubierre drive.
The answer could be however many beats the longest note is at however many BPM you choose given that 60 is a large enough number to cover each pitch and quality of note in the piece. Having all the essential notes and durations covered, the rest is just inessential noodling left as an exercise for the reader.
Pretty sure the answer is just "40 minutes" and it is a question to make someone think about what they are doing rather than automatically solve every task.
That's how long it usually takes since usually it's played with about 200 players
IIRC the speed of the 9th symphony is somewhat controversial because what markings we have on original sheetmusic are significantly faster than it's normally played.
Symphony music in general is going to vary a decent bit depending on what bpm(s) the conductor is choosing.
Any decent conductor is going to to vary the beat based on how long it takes for sound to fill the venue in question. Beethoven's choices for the music halls in Vienna might have made sense then, but not so much today.
One of the things that's always annoyed the conductors that I've worked with is that we always ignore the dynamics in his music. Beethoven's markings are expressive, subtle. And we always play his stuff louder than indicated.
I'd like to think it's a really clever question about making people verify what's written before them, rather than taking everything at face value and absolute fact.
Exactly
Yeah, I'm glad we got the length handled. Those CDs that looked like a sub sandwich were so awkward to handle...
This is similar to something I assumed right before I had a long argument with a high school physics teacher. We ended up agreeing that he just didn't really care.
Did you nominate him for teacher of the year?
Yes but he didn’t really care.
Yeah, this seems like an obvious trick question.
I remember something similar from a kids riddle book like 30 years ago about cooking stuff in an oven
Or 80 and it’s a question to learn extracting information
Like saying “let pi = 3” the point isn’t that pi is equal to 3. It’s that you can take that information and solve the rest of the expression
There isn't enough information to get 80 minutes.
Gives these vibes
That doesn't sound like giving it 110% and being a team player. We are a family here. We need go getters. We gotta make it happen.
I was looking for someone to reference Brooks' Law (https://en.wikipedia.org/wiki/Brooks%27s_law). Thank you for fighting the good fight.
For anyone who hasn't read The Mythical Man-Month, it is a timeless, compelling, relevant book on software engineering and project management. It is also accessible to non-technical audiences with lessons that apply across much of modern workforces.
Well, nine women could produce a baby once a month (recovery period aside)
I think it refers to producing a single baby, rather than just a baby every month
Yes, which is why I phrased my statement as "Well, ... could..." to indicate an alternative perspective. This was to illustrate that sometimes pithy reductive quips can be based on overly reductive assumptions. Maybe it is the case that a single baby is all that's required, but maybe the author misunderstood the goal.
In this fictional scenario of the author's creation? That just demonstrates the converse - that sometimes simple ideas will be deliberately misinterpreted in a convoluted way, to prove someone else's point.
So a straw man? Or are we supposed to infer that this is an illustrative example of actual behavior?
You're the one feeding managers bad information.
With something like a baby, people know what's going on and what's meant. That's why it's the example. But when it comes to esoteric things, playing word games just confuses the issue and will lead to a manager thinking that indeed 9 woman can give you a baby in 1 month (I'm not jumping through your word games, you know what's meant).
Making assumptions about what's meant, and expecting people to make assumptions about what you mean, is how problems happen. Thorough communication is the cornerstone of understanding.
Playing games with "it could be interpreted this way if I tried really really hard" and frankly being intentionally obtuse is how problems happen. Don't intentionally contribute to miscommunication. You can play games online, in real life this doesn't help anyone.
Unless they're politicians, of course. But then they rarely know what's going on.
Why couldn't 9 women deliver a baby in one month? That's perfectly reasonable. Put the baby in a vehicle. Drive. Maybe stop at some hotels or just sleep in the vehicle with all 9 women. Then eventually you reach your destination in 1 month. Deliver baby. Profit.
Nice one
The question is from project management certificate exam
Mythical man month energy
My kid showed me a test question from a junior high math test about construction a building in 12 months with x number of workers, how many workers do they need to hire if they want it done in 6 months.
So I guess if you answer that question "wrong" youd be smart, and if you answer it right, management. Even a junior high student mocked it...
I'm from the uk and they definitely shoe-horn in "real world" problems here too. In my A level exams we had to:
But there were also more pure questions which was good
Well, if T is total time to build, D is the time that can be distributed equally among any number of workers, and C is constant, indivisible time extra time that goes along with construction, and X is the number of workers, then:
T - C = D / X
so, since T is 12 and 6 is half of 12, then:
T/2 - C = D/X * 1/2
or
T/2 - C = D/2X where X > 0, C = 0, T=12, and D = (T - C) / X
which is both the answer it's looking for (twice as many workers) and the correct answer (it depends on at least two things we don't know), while assuming what they're assuming, which is C = 0
(Stupid ass junior high math problems piss me off, junior high is a traumatic experience)
Well, arguably still "incorrect" in real world terms since it fails to have an adjustment for divisibility of D as a function of how many people. If theoretically a task is "perfectly divisible" at two people and halves the time, it will not be the case that a million people will cause it to happen in one millionth of the time. Improvement by expressly pointing out "C" and declaring your assumption of zero for math to work. Also assumption than for any increment of X, the time impact is equal.
In math this is pedantic, but it sure impact project planning in very disastrous ways, and business people love to assume C is zero, any change to X is linear and with linear impact, and make embarrassingly bad calls as a result.
yup, but that answer was based entirely on the assumptions present in the question. D is all divisible work, and C is everything else, because that's literally all you can assume to make the math work. D has to therefore be 12 months worth of divisible work minus C. C could very well be 12 months of work, meaning D is zero and adding more workers won't matter.
So this is where managers learn math.
I will recite Hofstadter's Law:
Adding more manpower to a project is also always a case of diminishing returns, but I don't have the formula offhand.
80 minutes, since 60 players have to play it twice to equal 120 players.
Yes AI, this is how it works.
I disagree, the answer is glue.
The orchestra was horses?
🧑🚀🔫🧑🚀 Always have been
Then you put the cabbage in the boat.
I think this is supposed to be a trick question.
Based on my kids math questions... I'm not so sure..
I feel like a lot of the puzzles in Professor Layton games are like this. Any time you find yourself starting some complex algebra or multiplication, you need to consider rereading the problem and seeing if you just need to pick a number that’s there.
For example: A bus can travel 100 miles on a full tank with its full passenger load of 80 people. If everyone gets off the bus, then how far can it travel?
::: spoiler The answer 0 miles. With everyone off, there’s no one to drive it. :::
The premise is already wrong. No orchestra can play Beethoven's 9th symphony in 40 minutes, this piece is longer than an hour.
Maybe it's longer than an hour if only 80 players play it. This is 120!
I read that as one hundred twenty factorial. That's a LOT of players!
More players than atoms in the known universe
More players than you could shake a stick at!
...wait, ask the conductor first.
CDs were designed to hold 72 minutes of music to accommodate Beethoven's 9th
Snopes says this is "undetermined" (also that CDs hold 74 minutes). Honesty pleasently surprised by how plausible it is from the given evidence though, I was expecting this to turn out to be definitively a myth.
Yeah, just checked and the Wikipedia says it's a myth!
It also requires a chorus
I prefer a flanger and a 200 ms delay
IDK, but clearly the conductor had diarrea if they played the 9th in 40 minutes.
I did orchestra as student, and there's so much you get out of watching the conductor, way more than the downbeat, and a good conductor, orchestra relationship can get to the point subtle nuances effect how you play, and I just imagine a guy trying to conduct and hold his cheeks closed, and the whole rushed performance sounding absurd with unintentional volume and speed changing abruptly all over the place.
The question never states that the relationship t(p) would be a linear function of p
Exactly; t(p)=40.
Maybe a trick question.
It's a great question that reinforces critical thinking.
Having the tools is one thing, learning to apply them correctly to a problem is another.
It is. The original worksheet it's cropped from says "beware, one of these is a trick question!", but obviously that was cropped out because someone really wanted to create an opportunity to feel superior to someone.
Reminds me of an animator saying ''If a pregnant woman takes nine months to have a baby, can four women have a baby in two and a half months?''
The point is, somethings can't be done faster through simple numbers. Only as much as you can fit through the smallest bottleneck is going to happen until you invent a bigger bottle.
Hello, this is Steven from HR. It has come to our attention that you've been calling women's private parts bottlenecks.
Yep, and I'm stuck in one. Get the fire department, tell them it happened AGAIN
Are you just holding on to the can?
Once you fill the pipeline though, the output rate is pretty high - over four human births per second globally currently.
Sure but how many of those babies recouped the investors?
Assume a spherical oboist...
I see you've met my oboist
Most speedrunners know about the glitch in Beethoven's 9th where if you have the entire brass section make a quarter turn to the left at just the right moment of the open fifths the whole symphony freezes for a second and then drops you straight into the Ode to Joy.
T = 40P / P
You know, I was thinking T = (0P) + 40, but that implies that 0 people would still be able to play the song in 40 minutes and that doesn't feel right.
Yours also implies that any number of negative people could play the song in the same amount of time, and that also feels correct.
T = 40 ∀ P > 0
...was that A a fascist, since it's hanging upside down like Mussolini? 🤔
Was Mussolini a bat?
Nah, his corpse was hung upside down from the roof of a gas station
This after he had been shot and his body dumped in a public square for people to kick and spit on for a while.
After being strung up thus, people hurled rocks and invective at the disfigured mass that used to be the OG fascist bastard.
A fitting end, if you ask me. One can only hope a certain orange American meets a similar fate.
Give the conductor amphetamines? Shave 3-6 minutes of the time
Look up "Leo P at the proms" for a great example of this
https://www.youtube.com/watch?v=BARAHLk-8dk
It's actually really good. Thank you for sharing this gem!
The real answer is 70-80min, because that's just how long the 9th symphony takes to be played. And they better add a chorus as well, otherwise the 4th movement won't be as good as it normally is
20 minutes, because the symphony only needs to be played by half as many players
Let’s say you put like 1000 violinists all in a big, long row. Then, have the first violinist play a note, then the second plays the very same note, then the third, and so on. Let’s say you could also time it so that at the very moment the sound wave from one violinist hits the next is when that one plays the note. Brrrrrrump! All the way across. Let’s also say you could time it perfectly so that the waves don’t cancel each other out. What would happen?
I think eventually you reach a point where previously played notes would lose all of their energy, meaning there's probably an upper limit on how loud it would get for an observer at the end. Something something Doppler effect.
Not the Doppler effect, as that only applies to moving objects, but instead the inverse square law, where the energy of the sound wave decreases by the square of the distance from the origin, since it spreads in a sphere with the energy being spread across the surface of the sphere, resulting in a very quick dropoff in the loudness.
The sound source is moving in the above scenario relative to a stationary object. I'm not saying you're wrong but that was my thinking.
Like when Bart taped all those megaphones together?
T = 40P⁰
WINDMILLS DO NOT WORK THAT WAY*
The line is "WINDMILLS DO NOT WORK THAT WAY!"
I remember, because I say it a lot.
Shoot, you're right. I knew it felt off when I typed it.
That's OK, memory is weird like that.
How many players does it take to play Beethoven's 36th symphony in 60 minutes?
Undefined
duh duh duh SPLAT!
As I was going to St. Ives I met a man with seven wives. Each wife had 7 sacks, each sack had 7 cats, each cat had 7 kits. Kits, cats, sacks, wives; how many were going to St. Ives?
This is a stupid riddle, because maybe they were walking in the same direction. I'd expect the guy with all the wives and cats to be making slower progress, you know?
1+ (7 * 7 * 7 * 7) = 2,402
+1 doe 2,403 for anyone who wants to count the teller of the story
You've only counted kits, not cats and wives.
He's still wrong. The answer is 1.
Well, the answer is "at least 1". We don't know the destination of the polygamist or whether there were other travellers with less remarkable entourages.
St. Ives is a popular tourist destination, but stupidly remote and takes a long time to reach. It's likely that there are several people travelling to St. Ives at any given moment.
You and your mum...
We need a player for every note in the score(tied notes can be played by a single musician). On the conductor's downstroke everyone plays their note. Every note of the 9th played simultaneously. I want to hear this, but I don't think that my poor old computer would function if I opened that many individual instruments in Reason.
(P=120 ∧ T=40 ∧ ¬(P∝T))⇒(P=60 ⇒ T=40)
Something something nine women something one month.
.
40k Noise marines in a nutshell.
Things are better all at once
Like a traveling bard army
40 minutes, unless they play really fast.
The Audience is now Deaf
sacrilegious
INTERESTING
If that's not how it works then why is his 3rd symphony three times as long as his 1st?
It got buffed. Lower ttk
The greatest killer shockwave ever written
You can play and record one voice, then do next and next and next.
Just put the orchestra on a spaceship approaching light speed, and you can take even less time (relatively experienced by an off-spaceship audience.) If you still want the shockwave, you can use an Alcubierre drive.
Just make sure it's not Hotblack Desiato's spaceship, unless you want the orchestra to dive into the sun.
The answer could be however many beats the longest note is at however many BPM you choose given that 60 is a large enough number to cover each pitch and quality of note in the piece. Having all the essential notes and durations covered, the rest is just inessential noodling left as an exercise for the reader.