

dimis
Responsible
Supreme Hero
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posted November 07, 2008 10:15 AM 


I know this is not an argument. And I am not talking about "one room". Instead you calculated (in your head though..) the rate at which each guy works per hour ... That "per hour" is the reduction to "1". I never used that ...
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dimis
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Supreme Hero
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posted November 07, 2008 10:18 AM 


So, Celfious, what did you want to achieve by dividing by two, then adding them up, and again dividing by two. Try to justify the steps you make with words, otherwise few can follow anyone...
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JollyJoker
Honorable
Undefeatable Hero

posted November 07, 2008 10:19 AM 


Ok. Since the 4point problem is actually a stateofmind problem and there should be a real mathematical problem as well, I'll give you one I hope you'll find interesting, especially because it has to do with Heroes 5.
I've always been a sucker for probability mathematics, I think from the day on I realized that it may help you not to be taken for a fool. A rather easy example is this: a game is offered to you. Simple double or nothing, you'll get to cast three dice once (dice are not manipulated). You'll win on any number of rolled 6s, you lose if you don't manage one.
While this may sound like a fair offer for the "mathematically uneducated", probability shows that in fact the dice are loaded against you and for the guy who makes a business out of this game.
On to Heroes 5:
Maybe you know  or maybe not  I was involved in HoMM5 beta testing. As it was, I wasn't all too pleased with the way the magic system was shaping up, claiming too predictable strategies if all races except Academy would be given 2 guaranteed schools.
I actually came up with another solution that I got the pleasure to discuss with Fabrice and the then chief designer. It was based on the fact that every guild level was designed to be able to show 4 spells on each level.
My suggestion now was the following: On building a mage guild level, the guild would show ANY 4 spells out of the 8 available ones, with the PLAYER being able to pick the allowed number for the level (with the Library allowing one more pick, making a pick unnecessary for the first 3 levels for Academy), that would actually STAY to be learned.
After some discussion the suggestion was dismissed, claiming that as soon as a second town would be involved players would have mostly every spell they wanted to have. I didn't have the math then, obviously, in direct answer, so I just countered with hinting on Necropolis and how having more than one town (of different alignment) would tilt the balance there, but to no avail.
So here is the task then: 1) Compare the probabilities for the actual and the suggested system for getting the spell CONFUSION, starting with ANY of the initial 6 towns and getting ANY 2nd town early on a map.
For clarification: You will have to make different cases for the ACTUAL system and the differences in towns. Probabilities for actually GETTING Confusion in the SUGGESTED system are the same for every town including Academy, though (which should be clear).
For towns that don't come with guaranteed Dark Magic spell in the actual system, the mechanism is that the 3rd (and 4th for Academy) are guaranteed picks from the 2 nonguaranteed schools.
2) For the actual system, each town has 2 guaranteed schools, and the probability to get exactly 1 spell each in both schools if you have 1 town is exactly 100%. What probability do you have in the suggested system in each single town to get ar least one spell of any school for each level?
Edit: For clarification. Here the question is for the probability you have for the suggested system in any town to find at least ONE spell of one SPECIFIC magic school on each level of the guild.
3) What about the probabilities of getting ANY 5 spells of ANY school in one town. And what about the probabilities of getting NONE or ALL of the spells of any one school in one town for the suggested system?
For clarification: Here (and this is the most difficult to find out) I want to know the probability of getting EXACTLY 5 spells of one specific magic school out of such a guild, no matter the mage guild levels. (If you can answer that you will be able to compute the probabilities for every other number of spells between 0 and 10 as well.)


Celfious
Responsible
Legendary Hero
Rat whisperer

posted November 07, 2008 10:22 AM 


Ok 2 different guys painting the same room, one paints 5 hours, the other takes 3 hours. Since we're putting them together I (lets take a simpler route) added them then divided by 2 coming up with 4 hours. The voices in my head told me to divide by 2 again no just kidding, I honestly don't know why I divided by 2 again. I had a valid reason too but its to complicated and makes no sense on the mathematical light of things.
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Asheera
Honorable
Undefeatable Hero
Elite Assassin

posted November 07, 2008 02:51 PM 


@Celfious: That's not how it works at all. You don't have to take the average
It's explained in the previous page how to do it.
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JollyJoker
Honorable
Undefeatable Hero

posted November 07, 2008 02:57 PM 


Nah, you forget human synergy.


TheDeath
Responsible
Undefeatable Hero
with serious business

posted November 07, 2008 03:03 PM 


Is the first problem still active? I didn't see Corribus posting.
Father takes 3 hours.
Son takes 5 hours.
In 1 hour, father paints 1/3 of the room, son paints 1/5.
How many hours to paint the full room (result is 1)?
(1/3 + 1/5)*x = 1
x = 1 / (1/3 + 1/5) = 1 / (8/15) = 1.875
So it's like TA said
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Asheera
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Elite Assassin

posted November 07, 2008 03:03 PM 

Edited by Asheera at 15:08, 07 Nov 2008.

Quote: 2) For the actual system, each town has 2 guaranteed schools, and the probability to get exactly 1 spell each in both schools if you have 1 town is exactly 100%. What probability do you have in the suggested system in each single town to get ar least one spell of any school for each level?
For level 1, 2 and 3 you have a chance of 50% for a spell from a specific foreign school to popup. For level 4 and 5 it's 0% (without Library)
So, to get at least one spell from the X school (X is foreign here), the probability is 87.5%
To get three spells from X school at each level, the probability is 12.5% (the opposite as in the previous case)
(ok there are exceptions because of TotE Spells (Sorrow, etc), but that makes it too complicated )
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JollyJoker
Honorable
Undefeatable Hero

posted November 07, 2008 03:23 PM 


Err, you misunderstand that. The "suggested system" is the spell system I suggested. Please read the post again.


Asheera
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Elite Assassin

posted November 07, 2008 03:24 PM 


Ah sorry I thought you were referring to how it is now.
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Gnoll_Mage
Responsible
Supreme Hero

posted November 07, 2008 03:32 PM 


My immediate thought was 2.5 hours  correct if you add the condition that each person can paint at most half of the room.
I worked it out in a very silly way  starting by working out how much of the room the faster guy paints. This appears to be a sensible method in general  the faster guy paints five `squares` for every three of the slower guy (just invert the numbers), so in total, the faster guy paints 5/(5+3) of the room. You just multiply this by 3 to get the right answer (since he paints a whole room in 3 hours). However, I didn't realise this at first and ended up having to find the limit of a geometric series...
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dimis
Responsible
Supreme Hero
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posted November 07, 2008 03:39 PM 


There is still a 12 or 13yearold simple solution noone suggested.
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JollyJoker
Honorable
Undefeatable Hero

posted November 07, 2008 03:45 PM 


Yeah, lol. EIGHT hours.
First John paints it for 3 hours, then James follows suit for 5 additional hours, making it 8 hours.


TheDeath
Responsible
Undefeatable Hero
with serious business

posted November 07, 2008 03:46 PM 


LOL that wasn't a math problem that was a riddle
I thought they painted cooperatively.
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Domzilla
Tavern Dweller

posted November 07, 2008 03:52 PM 


Hmm i would say about 7 hours.
John only figures it would take him about 3 hours and his son 5 hours. is he a painter? or does he know his or his sons full painting ability? it will take at least two coats two paint it, maybe even three (which would mean about another 3 hours or so...), not including time to let the paint dry. And if he wants to respray his roof and cornices (assuming he has them) then it can take a while...
Maybe they will paint for too long and inhale too much and die??
Either way i reckon i can do a better job than John, sucked in mate.


Corribus
Hero of Order
The Abyss Staring Back at You

posted November 07, 2008 04:05 PM 

Edited by Corribus at 16:09, 07 Nov 2008.

Sorry for the delay.
TA was the first to get it correct. An overwhelming majority of people say "4 hours", but they're not really thinking critically about the problem. You have to use the assumption that the most obvious way for the painters to paint the room is to do so simultaneously.
Here is a full explanation, which I wrote for someone who didn't understand why the answer isn't 4 (or 2) hours:
The answer is not 4 hours, unless you make the assumption that they aren't painting simultaneously. It's a deceptively complex problem, but it's very easy to solve once you understand how the painters paint a room. Think of it this way.
If there are two men painting a room, each man only has to paint half a room. So, it will take the 5hour man (James) 2.5 hours to paint his half and the 3hour man (John) 1.5 hours to paint his half, which might lead you to say 4 hours. But, it's not reasonable to assume that they aren't working at the same time. I.e., John doesn't wait until James is finished with James' half before John begins his half. Thus, clearly it will take less than 4 hours to paint the room, because they're painting at the same time.
Ok, so then you say, well they both start at the same time. In 1.5 hours, John is done with his half, and in 2.5 hours, James is done with his half, so the whole house is painted after 2.5 hours. But, it's also not necessarily reasonable to assume that after John is done, he just sits around while James finishes the rest of the room. I.e., they're painting simultaneously until the room is finished.
So, again assume they both start at the same time. In 1.5 hours, John has finished his half of the room. At this point, James has only finished 60% of his half (30% of the whole room). 80% of the entire room is finished. Now, they both start on the remaining 20%. Of this 20%, each will start to paint half, or 10% of the whole house. It takes John 18 minutes to paint his 10% of the room (3hours or 180 minutes for the whole room, therefore 18 minutes for 1/10 the room). In 18 minutes that it takes John to finish his 10%, James finishes only 60% of his 10% (6% of the total room), leaving 4% of the entire room. So far, it has taken 108 minutes to paint 96% of the room. There is 4% remaining. Again, they split the remaining area. John paints 2% of the whole room and James paints 2%. It takes John 3.6 minutes to do this. In that amount of time, James only gets 60% of that amount of area covered, or 1.2% of the whole room, leaving 0.8% remaining. Now, 111.6 minutes have expired. You can extrapolate this out to infinity, or realize you're dealing with rates.
For example, assume the house has X amount of area, measured in ft^2.
James's painting rate is X ft^2/5 hours or (X/5) ft^2/hour.
John's painting rate is X ft^2/3 hours or (X/3) ft^2/hour.
So, the total rate of area being painted is the sum of their individual rates or (X/5 + X/3) ft^2 per hour. The total area needed to be painted was X ft^2. The total area divided by the rate gives you the total time of painting, or 15/8 hours, which is approximately 113 minutes.
The problem leaves some important information out about how the painters are painting the room, but you have to believe that any normal pair of people would be painting simultaneously, so 113 minutes is the best answer.
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broadstrong
Promising
Known Hero
Level 20 Vassal of Light

posted November 07, 2008 04:19 PM 


@Corribus,
Well explained. The idea of ratio, rate and proportion is the gist in solving such questions (and from what I know, many students have problems in understanding these concepts, so questions such as those you have posed becomes problematic to them).
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JollyJoker
Honorable
Undefeatable Hero

posted November 07, 2008 04:21 PM 


That's a typical Calvin & Hobbes math problem, by the way that might end with either a very practical or very creative solution.


Corribus
Hero of Order
The Abyss Staring Back at You

posted November 07, 2008 04:28 PM 


The goal when educating students is, of course, to get them to think critically about how to solve problems, rather than just plugging numbers in and getting a new number that is "right", and then getting an A on the test. My own teaching philosophy is that learning how to approach a problem is more important than getting a "right answer". As JJ has written, this problem has a number of right answers, depending on how you assume that the painters paint the room. The key thing for students is to identify what those options are, and then figure out how that affects the outcome.
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I'm sick of following my dreams. I'm just going to ask them where they're goin', and hook up with them later. Mitch Hedberg


TheDeath
Responsible
Undefeatable Hero
with serious business

posted November 07, 2008 04:29 PM 


I think Corribus thinks too complicated, my (intuitive) solution is so much easier to explain
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