Math Fun

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

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Re: Math Fun

Postby James S Saint » Thu Jul 23, 2015 8:21 pm

phoneutria wrote:Let me try and be thorough :)

Is it even worth putting it in tabs anymore?
If you have a chart on the wall and say these colors are included in the problem, and you can't see one of them, obviously that is the color of your band. You would get up and leaving thinking that this is probably the most boring math problem ever, although perhaps more suitable to your objection.
But now you are gone and the others are sitting there trying to figure out when to stand up. What should they do?
The person who can see a color with only one person wearing it must assume that they need to get up and go, because if anyone there was not able to see a color on the chart, they would have already left. From there, in sequence, people who can see 2 people with the same color, then 3, then 4...

So, not having that first person who can't see any headbands with one color of the chart only changes the problem slightly by making it less boring. If you take down the chart, you still have a chart composed of all the colors you can see. Those colors of the headbands around you are your color group. If you can't see a color, it is not in the group. The sequence begins to iterate at 2.

There were two objections being discussed.
1) Is it necessarily true that you must be able to see your own color on someone else?
2) Having proposed a possible means for solving the puzzle, can it be proven that it is impossible to solve the exact same puzzle arrangement by any other means?

I quickly dispatched (1) merely by showing that a known or famous color chart would allow a person to guess at his color without ever seeing it on anyone else.

Objection (2) is the one that I propose makes the puzzle invalid. You propose a particular means to solve the puzzle. Now prove that no other means could ever be proposed that would also solve the same puzzle arrangement. Without being able to prove that no other means could ever exist, the proposed solution cannot be used and thus does not actually solve the puzzle. For example, perhaps there is a different color chart of which you were not aware that implies a different missing color or perhaps merely a more sophisticated math model would imply a different one of the colors that you do 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

Postby James S Saint » Thu Jul 23, 2015 10:42 pm

Perhaps let me address this issue in a different manner.

Puzzle Key Question:
Is there a color arrangement for that scenario that would allow for the existence of an algorithm to resolve what color each person was wearing and also can be proven to be the only possible algorithm for that color arrangement?
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

Postby phoneutria » Fri Jul 24, 2015 4:55 pm

James S Saint wrote:There were two objections being discussed.
1) Is it necessarily true that you must be able to see your own color on someone else?
2) Having proposed a possible means for solving the puzzle, can it be proven that it is impossible to solve the exact same puzzle arrangement by any other means?

I quickly dispatched (1) merely by showing that a known or famous color chart would allow a person to guess at his color without ever seeing it on anyone else.

Objection (2) is the one that I propose makes the puzzle invalid. You propose a particular means to solve the puzzle. Now prove that no other means could ever be proposed that would also solve the same puzzle arrangement. Without being able to prove that no other means could ever exist, the proposed solution cannot be used and thus does not actually solve the puzzle. For example, perhaps there is a different color chart of which you were not aware that implies a different missing color or perhaps merely a more sophisticated math model would imply a different one of the colors that you do see.


You did not quickly dispatched 1 because the problem does not give you a chart. It doesn't state "consider a group of colors (blue, green, yellow, orange, red)". This information is not present, there is no color chart as a given in the problem premise. When the problem starts you don't have a closed group of colors to work with. Part 1 of the problem is constraining all possible colors down to a group.

As to 2, it is evident that there is no other way to solve this puzzle. Assuming that the group of colors consists only of colors that you can see is necessary because otherwise you do not have a constrained group.
Once you have a group, you can write an algorithm:

Code: Select all
for (bell = 1; bell>numberOfLogicians; bell++) {
    for(numberOfColor = 1; numberOfColor>bell; numberOfColor++){
        if (numberOfColor == bell){
            System.out.println("logicians who can see this numberOfColor have to get up and leave");
            //TODO: write a method for making logicians leave.
        }
    }
}


(numberOfLogiciansWearingHeadbandOfTheSameColorThatALogicianCanSee would be the correct name, but to make it readable I called it numberOfColor)
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Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 6:06 pm

phoneutria wrote:You did not quickly dispatched 1 because the problem does not give you a chart. It doesn't state "consider a group of colors (blue, green, yellow, orange, red)". This information is not present, there is no color chart as a given in the problem premise. When the problem starts you don't have a closed group of colors to work with. Part 1 of the problem is constraining all possible colors down to a group.

The puzzle doesn't have to state that chart, just like it didn't state the number of repeated colors. The challenge of the puzzle was to consider all possible color arrangements in order to find any that would allow the prediction. We are looking for any possible arrangement of colors that would allow the prediction of the color of an unseen band. If you know of the primary color chart and you see one of each of those colors except one, you can predict that one. And you can claim that "it is evident" that the color could not be predicted any other way.

phoneutria wrote:As to 2, it is evident that there is no other way to solve this puzzle.

"It is evident" (aka. "I can't think of anything") is the "turtles all the way down" solution. It does not constitute a premise for a logical deduction, merely a probability based upon the person's intelligence.

You have to be able to prove that the proposed algorithm is the only possible means of solving the problem, else it is not a valid solution. You can't merely state, "it is evident".
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

Postby phoneutria » Fri Jul 24, 2015 6:23 pm

It is evident that you can't know a color that you can't see.
phoneutria
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Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 6:34 pm

phoneutria wrote:It is evident that you can't know a color that you can't see.

Okay then;
It is evident that you cannot predict a color that you can't see.

And it is evident that it is turtles all the way down.
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

Postby phoneutria » Fri Jul 24, 2015 7:00 pm

James S Saint wrote:
phoneutria wrote:It is evident that you can't know a color that you can't see.

Okay then;
It is evident that you cannot predict a color that you can't see.

And it is evident that it is turtles all the way down.



[-o<

It is evident that you cannot predict a color that you can't see.
Someone who can see your color (and all other colors present) states that the problem is solvable.
Therefore, you can see your color.
Last edited by phoneutria on Fri Jul 24, 2015 7:22 pm, edited 1 time in total.
phoneutria
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Posts: 3721
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 7:22 pm

phoneutria wrote:It is evident that you cannot predict a color that you can't see.
Someone who can see your color states that the problem is solvable.
Therefore, you can see your color.

That would constitute a prediction. [-X
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

Postby phoneutria » Fri Jul 24, 2015 7:29 pm

I added (and all other colors present) to the post above.

Where is the prediction? It's an induction.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3721
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 8:09 pm

phoneutria wrote:It is evident that you cannot predict a color that you can't see.
phoneutria wrote:Where is the prediction? It's an induction.

Make up your mind.
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

Postby phoneutria » Fri Jul 24, 2015 8:24 pm

James S Saint wrote:
phoneutria wrote:It is evident that you cannot predict a color that you can't see.
phoneutria wrote:Where is the prediction? It's an induction.

Make up your mind.


It is evident that you cannot predict a color that you can't see.

Attempting to guess a color would be a prediction.

Someone who can see your color states that the problem is solvable.


He is not making a prediction because he can see all the colors.
He is giving you a clue that is an indication of what the color group contains.

Therefore, you can see your color.

Direct conclusion from the two sentences above.
Because you can see it, it isn't a prediction.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3721
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 9:12 pm

phoneutria wrote:
James S Saint wrote:
phoneutria wrote:It is evident that you cannot predict a color that you can't see.
phoneutria wrote:Where is the prediction? It's an induction.

Make up your mind.


It is evident that you cannot predict a color that you can't see.

Attempting to guess a color would be a prediction.

Someone who can see your color states that the problem is solvable.


He is not making a prediction because he can see all the colors.
He is giving you a clue that is an indication of what the color group contains.

Therefore, you can see your color.

Direct conclusion from the two sentences above.
Because you can see it, it isn't a prediction.

The one who said it, the Master, is not the one making the prediction.
YOU are, based upon what he said, what you see, and your guess that there is only one way to resolve such a puzzle.


And you still haven't proven that there is only one way to resolve that particular arrangement of colors. Saying "it is evident" does NOT constitute a proof. It was evident to people thousands of years ago that "it was turtles all the way down" because they couldn't imagine anything else.
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

Postby phoneutria » Fri Jul 24, 2015 10:40 pm

There are two ways to arrive at the answer, actually:
- arriving at the conclusion that your headband has the same color as another one in your field of vision.
- taking a guess at what your headband color is out of millions of possible answers.

The first one leads to an induction algorithm. The second one is not logic. Since the master said it is a solvable problem, one must conclude that guessing won't be required.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3721
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 11:03 pm

phoneutria wrote:There are two ways to arrive at the answer, actually:
- arriving at the conclusion that your headband has the same color as another one in your field of vision.
- taking a guess at what your headband color is out of millions of possible answers.

The first one leads to an induction algorithm. The second one is not logic. Since the master said it is a solvable problem, one must conclude that guessing won't be required.

Look at the reasoning that you are using for each of those:

1) "I can't think of any way to know my color other than to assume that it is one of those that I am seeing."

2) "ASSUMING that it is one of the colors that I am seeing, I CAN'T THINK OF ANY WAY to deduce my color other than by this one algorithm."

In BOTH cases, you are assuming based upon the fact that you can't [currently] think of any way to deduce your color other than the one way you learned.

In effect, it is like saying, "I know that I am right because I am too stupid to think of anything else!"

What if Science was run that way? "We think electricity works this way because we can't think of anything else."

The fact that such was so very often wrong, Science was developed around demonstrations so as to give more concrete evidence and not rely on people just being too stupid to think of anything else.
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

Postby phoneutria » Fri Jul 24, 2015 11:07 pm

You are asking me to prove that guessing a color can't be anything but guessing.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
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Re: Math Fun

Postby James S Saint » Fri Jul 24, 2015 11:27 pm

phoneutria wrote:You are asking me to prove that guessing a color can't be anything but guessing.

I am asking for you to prove your assertion that there is no other way possible other than what you have proposed.
"It is evident" is not a proof.
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

Postby phoneutria » Sat Jul 25, 2015 1:01 am

Just let me get clear on this. What you are asking me to prove is that you can't find out an unknown color from an infinite set of colors. Is that correct?

I gave my answer. The only way to find out a color (or an int, or a string, or etc) from an very large set is by guessing. This is a popular computational process called brute forcing.
I find that to be evident. Can you, please, explain why you require proof of that?
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
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Re: Math Fun

Postby James S Saint » Sat Jul 25, 2015 3:13 am

phoneutria wrote:Just let me get clear on this. What you are asking me to prove is that you can't find out an unknown color from an infinite set of colors. Is that correct?

No.

I am saying that whatever your proposed solution algorithm is, by whatever method it works, you absolutely must prove that no other algorithm could have worked in its place (given a specific color arrangement). That is the ONLY way to be able to choose what color arrangement is satisfactory, which would then cause the Master to be correct in his claim of resolvability.
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

Postby phoneutria » Sat Jul 25, 2015 3:53 am

If there is any other way to constrain the color group, I would like to hear it.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3721
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Sat Jul 25, 2015 4:39 am

phoneutria wrote:If there is any other way to constrain the color group, I would like to hear it.

What that says is "I don't know". And that is why it is not a "PROOF", but merely a probability (aka not deductive logic).
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

Postby phoneutria » Sat Jul 25, 2015 4:46 am

James, it is a fact.
phoneutria
purveyor of enchantment, advocate of pulchritude AND venomously disarming
 
Posts: 3721
Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby James S Saint » Sat Jul 25, 2015 5:11 am

phoneutria wrote:James, it is a fact.

"Turtles all the way down."
"The Earth is flat."
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

Postby phoneutria » Sat Jul 25, 2015 5:13 am

Edit: I did not mean to say that :)
phoneutria
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Re: Math Fun

Postby phoneutria » Sat Jul 25, 2015 5:46 am

I was thinking just now about situations in which you don't have a perfect sequence of numbers of people wearing the same color, and as far as I can tell the solution still holds. The only thing is that sometimes the bell rings and nobody leaves.
phoneutria
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Joined: Fri May 23, 2014 5:37 am

Re: Math Fun

Postby Ben JS » Sat Jul 25, 2015 7:53 am

These puzzles are on Wikipedia with solutions explained.
Formerly known as: Joe Schmoe

ben wrote:I think it is eloquently fitting that my farewell thread should be so graciously hijacked by such blatant penis waving. It condenses my entire ILP experience into one very manageable metaphor.
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