## Math Fun

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

Moderator: Flannel Jesus

### Re: Math Fun

Dang, left out the "One family has more children than all the other families combined." part.
phoneutria
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### Re: Math Fun

phoneutria wrote:Dang, left out the "One family has more children than all the other families combined." part.

Yes.

Arminius
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### Re: Math Fun

Arminius wrote:The reputable house.

A few families live in a house from which we know the following facts:

• More children than parents live in this house.
• More parents than boys live in this house.
• More boys than girls live in this house.
• More girls than families live in this house.

No family is childless, each has a different number of children. Every girl has at least one brother and at most one sister. One family has more children than all the other families combined.

How many families live in this house and how are they composed?

I feel like I must be missing something:
3 families, each with 2 parents:
p = 2 2 2 = 6
g = 2 0 2 = 4
b = 1 1 3 = 5
c = 3 1 5 = 9

Arminius wrote:The dice game.

Each round of a dice game consists of two fair dice; the result of one throw is the product of the thrown numbers. A game consists of 5 rounds.

Bob throws in the second round by 5 more than in the first, in the third round by 6 less than in the second, in the fourth round by 11 more than in the third, and in the fifth round by 8 less than in the fourth.

How many points did he score in each of the 5 rounds?

1 3 = 4
2 7 = 9
3 4 = 7
4 1 = 5
5 1 = 6

Carleas wrote:Even if we assume that this problem is flawed, the MI syllogism proves the canonical solution to the Blue Eye problem.

No. It doesn't. You keep thinking that just because you have an operable algorithm, you have the only possible solution. For all of that type of problem, you MUST prove that your proposed solution is the only possible solution, else it isn't a solution.

Carleas wrote:The trick isn't to find an assumption that works, but to find a deduction that does.

All of your deductions include an assumption that must be validated by being the only assumption possible in order to cause the puzzle to be solvable.

Carleas wrote:If we assume that there is one correct solution, then the Master is clearly intending to follow and enforce it. So this objection seems to beg the question. If there is a solution, then there's no need to prove that the Master is following it, that's a given. If there is no solution, or more than one solution, then the problem breaks down for reasons unrelated to the Master.

Proving that you have the one and only possible solution proves that the master is using it.

Definitely not true.

Carleas wrote:But I haven't found any, and you haven't presented anything like a syllogism showing an inconsistent conclusion. The simplest form of my SR argument seems clearly valid:
1) If any logician's headband were not one of the colors he can see, the problem would be impossible. - UNPROVEN ASSUMPTION
2) The problem is not impossible
Therefore
3) Each logician's headband is one of the colors she can see.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

James S Saint wrote:
Arminius wrote:The reputable house.

A few families live in a house from which we know the following facts:

• More children than parents live in this house.
• More parents than boys live in this house.
• More boys than girls live in this house.
• More girls than families live in this house.

No family is childless, each has a different number of children. Every girl has at least one brother and at most one sister. One family has more children than all the other families combined.

How many families live in this house and how are they composed?

I feel like I must be missing something:
3 families, each with 2 parents:
p = 2 2 2 = 6
g = 2 0 2 = 4
b = 1 1 3 = 5
c = 3 1 5 = 9

Well done, James.

James S Saint wrote:
Arminius wrote:The dice game.

Each round of a dice game consists of two fair dice; the result of one throw is the product of the thrown numbers. A game consists of 5 rounds.

Bob throws in the second round by 5 more than in the first, in the third round by 6 less than in the second, in the fourth round by 11 more than in the third, and in the fifth round by 8 less than in the fourth.

How many points did he score in each of the 5 rounds?

1 3 = 4
2 7 = 9
3 4 = 7
4 1 = 5
5 1 = 6

Last edited by Arminius on Sat Aug 22, 2015 4:14 am, edited 2 times in total.

Arminius
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### Re: Math Fun

The reputable house

Duh myself
2P
1B

2P
2G
1B

2P
2G
3B
phoneutria
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### Re: Math Fun

phoneutria wrote:The reputable house

Duh myself
2P
1B

2P
2G
1B

2P
2G
3B

Well done, Phoneutria.

Arminius
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Posts: 5732
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Location: Saltus Teutoburgiensis

### Re: Math Fun

The dice game

a
b = a+5
c = b -6
d =c + 11
e = d - 8

c= (a+5) - 6
d = [(a+5) - 6] + 11
e = {[(a+5) - 6] + 11} - 8
max total=12

Round d can only be 11+1.

a=2
b= 7
c=1
d=12
e=4
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming

Posts: 3402
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### Re: Math Fun

Arminius wrote:
phoneutria wrote:The reputable house

Duh myself
2P
1B

2P
2G
1B

2P
2G
3B

Well done, Phoneutria.

I just shuffled things around a little bit. I knew I couldn't have been too far off because of the limit on the number of sisters.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming

Posts: 3402
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### Re: Math Fun

Arminius wrote:What about the solution process?

ESP.
Arminius wrote:
1 3 = 4
2 7 = 9
3 4 = 7
4 1 = 5
5 1 = 6

Damn .. looking at my scratch work, it looks like I rewrote the whole puzzle ..
2 *5 =10
3 *5 =15
3 *3 =9
4 *5 =20
2 *6 =12
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

phoneutria wrote:The dice game

a
b = a+5
c = b -6
d =c + 11
e = d - 8

c= (a+5) - 6
d = [(a+5) - 6] + 11
e = {[(a+5) - 6] + 11} - 8
max total=12

Round d can only be 11+1.

a=2
b= 7
c=1
d=12
e=4

That is false.

Arminius
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Location: Saltus Teutoburgiensis

### Re: Math Fun

James S Saint wrote:
Arminius wrote:
1 3 = 4
2 7 = 9
3 4 = 7
4 1 = 5
5 1 = 6

Damn .. looking at my scratch work, it looks like I rewrote the whole puzzle ..
2 *5 =10
3 *5 =15
3 *3 =9
4 *5 =20
2 *6 =12

Well done, James.

Arminius
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Posts: 5732
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Location: Saltus Teutoburgiensis

### Re: Math Fun

Arminius wrote:What about the solution process?

Hey, my job is to answer questions. Your job is to figure out how I got the answers.

.. just be sure to always disagree at least once so that I have incentive to go check my work ...
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

lol... the product, not the sum!
Facepalm....
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming

Posts: 3402
Joined: Fri May 23, 2014 5:37 am

### Re: Math Fun

James S Saint wrote:
Arminius wrote:What about the solution process?

Hey, my job is to answer questions. Your job is to figure out how I got the answers.

Let me guess twice:

1) By reading, understanding, thinking, and calculating.
2) By finding the answers in the internet.

Arminius
ILP Legend

Posts: 5732
Joined: Sat Mar 08, 2014 10:51 pm
Location: Saltus Teutoburgiensis

### Re: Math Fun

Arminius wrote:
James S Saint wrote:
Arminius wrote:What about the solution process?

Hey, my job is to answer questions. Your job is to figure out how I got the answers.

Let me guess twice:

1) By reading, understanding, thinking, and calculating.
2) By finding the answers in the internet.

If I could look up the answer, I could look up the process for obtaining it.
I don't go to that trouble for mere games.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

James S Saint wrote:You keep thinking that just because you have an operable algorithm, you have the only possible solution. For all of that type of problem, you MUST prove that your proposed solution is the only possible solution, else it isn't a solution.

1) I've presented a logical syllogism, using mathematical induction, which is a method of deductive mathematical logic.
2) As we've already discussed, once you have a syllogism, you don't need to show that there are no other syllogisms (see e.g. the Pythagorean Theorem)
3) Even if it were the case that I needed to show there were no other solutions, for the MI problem I've provided a syllogism that shows that N islanders cannot learn their eye color before day N, so if there were another syllogism, it would produce the same result.

James S Saint wrote:
Definitely not true.

It is true for certain premises. If we assume X and ~X, we can conclude Y and ~Y. I'm saying that "this problem is not impossible" is an exotic premise that could similarly produce contradictory conclusions. I don't think it does, but much of your argument seems to depend on it.

James S Saint wrote:1) If any logician's headband were not one of the colors he can see, the problem would be impossible. - UNPROVEN ASSUMPTION

Right, but you'll notice that I only said that the syllogism is "clearly valid". The point being that a valid syllogism can be constructed using "this problem is not impossible" as a premise, and challenging you to show that the syllogism shouldn't be treated like any other.

Do you agree that "colors don't bear any logical relation to each other" is a true premise? Or do you have a similarly true premise that leads to a contradictory conclusion?
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Carleas
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Location: Washington DC, USA

### Re: Math Fun

Carleas wrote:
James S Saint wrote:You keep thinking that just because you have an operable algorithm, you have the only possible solution. For all of that type of problem, you MUST prove that your proposed solution is the only possible solution, else it isn't a solution.

1) I've presented a logical syllogism, using mathematical induction, which is a method of deductive mathematical logic.

Only AFTER you skipped over substantiating your most essential premise (your presumption of colors) as well as your presumption that a faster method of color discovery could not be used.

Carleas wrote:2) As we've already discussed, once you have a syllogism, you don't need to show that there are no other syllogisms (see e.g. the Pythagorean Theorem)

Carl, that is stupid. Why do you keep saying that? Do you not read criticisms of your propositions? That is just a dumb thing to say and I have explained why. Once AGAIN:
We are NOT talking about many proofs for the same outcome.

We are talking about the need to prove that there cannot be any other possible outcome, and thus no other possible algorithm/solution.

Carleas wrote:3) Even if it were the case that I needed to show there were no other solutions, for the MI problem I've provided a syllogism that shows that N islanders cannot learn their eye color before day N, so if there were another syllogism, it would produce the same result.

No, you have NOT. I showed you that everyone could easily leave after the second bell. You are simply not listening.

Carleas wrote:Do you agree that "colors don't bear any logical relation to each other" is a true premise?

No, it isn't.

It would be true if you made sense of it first, but as stated and knowing the context, I have to deny it. Colors have a natural relative ORDER (most often expressed as a frequency). An order isn't technically "a logical relation", but it is an association that can be used in a logic argument: "Green is between yellow and blue. Purple is between red and blue. Orange is between red and yellow."
One of the premises is that "it is solvable", so...

And also the presented colors CAN have a displayed order:
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

Procrastinating....

dice game
A=10 (2 and 5)
B=15 (3 and 5)
C=9 (3 and 3)
D=20 (4 and 5)
E=12 (2 and 6)

Solution process: I put it on a spreadsheet

phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming

Posts: 3402
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### Re: Math Fun

phoneutria wrote:Procrastinating....

dice game
A=10 (2 and 5)
B=15 (3 and 5)
C=9 (3 and 3)
D=20 (4 and 5)
E=12 (2 and 6)

Solution process: I put it on a spreadsheet

Well done, Phoneutria.

Arminius
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### Re: Math Fun

Did you post your method for that, and I missed it, Arminius? I'd like to see it, because I pretty much brute forced it.
phoneutria
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### Re: Math Fun

phoneutria wrote:Did you post your method for that, and I missed it, Arminius? I'd like to see it, because I pretty much brute forced it.
In your excel sheet you can place true/false statements for the critical concerns along with the calculated numbers. Then merely count from 1 to 36 and one cell will tell you when you have the right number ("10") by saying "TRUE". All of the other numbers will be already calculated.

What they are calling "quantum computing" works that way except they assign a different CPU to each number between 1 and 36 so that all possibilities are computed in parallel. The first CPU that registers a "TRUE" stops the process. In that way, the time it takes to calculate the answer is always as if you already knew the "10" to try first.

If this were 20 years ago, I would spend some time trying to come up with a way to combine logic and math so as to directly cause the "10" answer to pop out from a single, albeit very long, equation. But these days, my brain is too tired.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

### Re: Math Fun

phoneutria wrote:Did you post your method for that, and I missed it, Arminius? I'd like to see it, because I pretty much brute forced it.

I guess you mean the solution process.

1st round = x.
2nd round = x + 5.
3rd round = x + 5 - 6 = x - 1.
4th round = x - 1 + 11 = x + 10.
5th round = x + 10 - 8 = x + 2.

All possible throw combinations:

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36.

A possible combination in each round is only possible with x = 10:

1st round = 10.
2nd round = 15.
3rd round = 9.
4th round = 20.
5th rounde = 12.

So as I already said: Well done.

Arminius
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Location: Saltus Teutoburgiensis

### Re: Math Fun

Armie,

So your solution, as well as mine and James involve iterating from all possible values until one matches. That's what I wanted to know, if that is the way to go about it, or if there is a way to derive a formula that would arrive at 10 without trying all the possible results.
Thanks.
phoneutria
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### Re: Math Fun

James,

Carleas wrote:Your examples, such as the color wheel and pattern examples, involve at best educated guessing or scientific induction (as opposed to mathematical induction, which is a deductive method).

James S Saint wrote:I agree

So, there may be some scientific induction that can be done given your set ups, but there is no deduction that could lead the logicians to conclude their headband color.

Again, I submit that "colors don't bear any logical relation to each other". There is no syllogism of the type, "red, yellow yellow, blue blue blue |- green"

Moreover, 1) with regard to your first example, every other logicians would realize that the logician with the orange headband would have no logical way to conclude her headband color, and 2) with regard to your second example, we've already discussed how there are an infinite number of completions to any pattern.

To the rest, I've specified two parts to the problem: the Set Restriction (SR) part, and the Mathematical Induction (MI) part. The parts are distinct. The MI part takes as one of its premises what is proven in the SR part, but the logic of the MI part is just the logic of common knowledge that solves the Blue Eyes problem and its variations. The SR part is still under discussion, I haven't skipped it, I'm just giving you the MI syllogism and asking you to respond to it at the same time. It is, after all, a part of the solution on offer (not to mention that it is a widely accepted solution to the Blue Eye problem which you obstinately refuse to accept, and I think you should).
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Carleas
Magister Ludi

Posts: 6107
Joined: Wed Feb 02, 2005 8:10 pm
Location: Washington DC, USA

### Re: Math Fun

Carleas,
Carleas wrote:James,

Carleas wrote:Your examples, such as the color wheel and pattern examples, involve at best educated guessing or scientific induction (as opposed to mathematical induction, which is a deductive method).

James S Saint wrote:I agree

I told you that my examples were a reflection of your example, each merely making a convenient assumption that allows the puzzle to seem like it is solvable, even though in the final analysis, it actually isn't.

Carl, you are just doing as I said that you were going to do back at the beginning of this; repeat yourself over and over while ignoring my counter arguments (although you did manage to muster up the answer to one usually ignored question). You seem to be incapable of seeing the obvious but perhaps are merely wrapped up into an ego concern of one type or another. In either case, you appear to not really care of the truth of this matter and thus I no longer care to discuss it with you. Your "Blue-eyes" class of puzzles are not being validly addressed.

But Wiki is in error in many articles, so this one wouldn't be anything exceptional.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend

Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

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