## Search found 538 matches

- Thu Feb 01, 2018 8:42 pm UTC
- Forum: Logic Puzzles
- Topic: The Goddess, the Villagers, and the Traveler
- Replies:
**16** - Views:
**3309**

### Re: The Goddess, the Villagers, and the Traveler

HeroSpirit, you seem to be misunderstanding my point. Saying "None of the villagers are aware of rule #4." does not specify what you actually mean by it. Think about the goddess/villager actions as living in some infinite set of possibilities. You have enumerated to us a subset in which th...

- Thu Feb 01, 2018 1:33 am UTC
- Forum: Logic Puzzles
- Topic: The Goddess, the Villagers, and the Traveler
- Replies:
**16** - Views:
**3309**

### Re: The Goddess, the Villagers, and the Traveler

I think the first point Yat brought up still holds. HeroSpirit seems to be implying that the villagers know all the rules, but are just unsure if Rule 4 is true or not. That is not equivalent to the villagers not knowing about Rule 4 at all. Just because the villagers don't know she has powers beyon...

- Thu Oct 05, 2017 7:10 pm UTC
- Forum: Mathematics
- Topic: Estimating Max with Only Definite Integrals
- Replies:
**14** - Views:
**3088**

### Re: Estimating Max with Only Definite Integrals

arbiteroftruth, I tried your strategy (with one oracle). It definitely isn't worse than the naive solution. However, I don't see much improvement either. I think the problem is the likelihood of eliminating a section is the probability that one section has n times the energy of the other, where n is...

- Tue Oct 03, 2017 7:20 pm UTC
- Forum: Mathematics
- Topic: Estimating Max with Only Definite Integrals
- Replies:
**14** - Views:
**3088**

### Re: Estimating Max with Only Definite Integrals

No, the samples are stored in RAM. So I can access them multiple times. In fact, that is mainly why I think my current solution is suboptimal. The problem is not the accessibility but rather the time required to go through each sample looking for the max. Through the oracle (which pre-processes the ...

- Tue Oct 03, 2017 5:25 pm UTC
- Forum: Mathematics
- Topic: Estimating Max with Only Definite Integrals
- Replies:
**14** - Views:
**3088**

### Re: Estimating Max with Only Definite Integrals

This is part of a larger system that I want to optimize. The system is my assignment. The naive algorithm I gave works, but I'm dissatisfied with the performance. If it helps, f(x) is actually a sampled signal, but at very, very high sampling rate. My oracle is just summing over some interval very e...

- Fri Sep 29, 2017 8:28 pm UTC
- Forum: Mathematics
- Topic: Estimating Max with Only Definite Integrals
- Replies:
**14** - Views:
**3088**

### Estimating Max with Only Definite Integrals

Hi guys! It's been a while. I've hit a problem in my work that I could use a little help in. Unfortunately I cannot divulge the full details, so I'm formulating it as a purely mathematical problem. The Problem: I have a function f(x) that is defined over some real domain x = 0 to n, where n is known...

- Mon Nov 21, 2016 12:39 am UTC
- Forum: Logic Puzzles
- Topic: Hidden Cards
- Replies:
**5** - Views:
**3238**

### Re: Hidden Cards

I suspect they should be trying to maximise the score (by making as few incorrect guesses as possible), but you don't actually state this. Oops, yeah. It was implied, but I should have stated that. If I were playing, I would start by making a "guess" of my own blue number. I would then st...

- Sat Nov 19, 2016 3:17 am UTC
- Forum: Logic Puzzles
- Topic: Hidden Cards
- Replies:
**5** - Views:
**3238**

### Hidden Cards

A group of 10 logicians have been challenged by a puzzlemaster to play a game. "I have here two sets of 10 cards, each with cards numbered 1 through 10. As you can see, one set is colored blue and the other is colored red. I will deal a blue card and a red card to each one of you. The red card ...

- Fri Jul 15, 2016 5:52 am UTC
- Forum: Logic Puzzles
- Topic: Monty Hall-ish Problem
- Replies:
**4** - Views:
**2897**

### Monty Hall-ish Problem

You are playing a game with a standard deck of 52 cards. The dealer draws three cards. Looks at them, then places them face down before you. He then draws a fourth card and puts it face down without looking at it. You are given two choices: take first three cards or take just the fourth card. You wi...

- Sun Jun 12, 2016 9:10 pm UTC
- Forum: Serious Business
- Topic: Trolley Problem
- Replies:
**349** - Views:
**63135**

### Re: Trolley Problem

I merely claimed that I'd like to live among people who chose {this thing}. Call it what you want, but that's about as close to "morally right thing" as you can get from someone that believes in moral relativism. I think the fundamental question we have to ask ourselves is "why is ki...

- Mon Mar 28, 2016 7:40 pm UTC
- Forum: Mathematics
- Topic: Need help with non-linear Diophantine
- Replies:
**10** - Views:
**2589**

### Re: Need help with non-linear Diophantine

Thank you both for the help! Looks like I'm in over my head on this problem. You guys offered much need insight. Cauchy, the reformulation you mentioned was indeed an IMO problem. In fact, it showed up on Wikipedia's Vieta Jumping page! The IMO problem only asked for a proof that d is a perfect squa...

- Mon Mar 28, 2016 12:34 am UTC
- Forum: Mathematics
- Topic: Need help with non-linear Diophantine
- Replies:
**10** - Views:
**2589**

### Need help with non-linear Diophantine

I'm trying to solve the following system over integers a,b,c,d: c+b = a*d c*b = a 2 - d There are only two equations for four unknowns, so I expect to have two degrees of freedom in the solution. However the only solutions I've found so far is: {a = any integer, b = a 3 , c = 0, d = a 2 }, which onl...

- Wed Mar 16, 2016 2:58 am UTC
- Forum: Science
- Topic: Moon formation effect on Earth's orbit
- Replies:
**10** - Views:
**2569**

### Moon formation effect on Earth's orbit

The most accepted theory for how our moon was formed is that another proto-planet crashed into proto-earth and spewed rocks into orbit around earth. These rocks accumulated and later became the moon. I'm curious about what that collision did to earth's orbit. Clearly earth was already orbiting prior...

- Sat Mar 12, 2016 10:44 pm UTC
- Forum: Mathematics
- Topic: does every unit length curve lie inside the semicircle?
- Replies:
**12** - Views:
**3262**

### Re: does every unit length curve lie inside the semicircle?

I think the reasoning for Cradarc's Claim 3 is faulty. Yes, the curve has to connect P, Q, and R, but you haven't shown that it has to do it within the sector. We don't have to show it is contained in the sector because we are looking for the minimal length. A path that isn't contained in the secto...

- Sat Mar 12, 2016 10:16 am UTC
- Forum: Mathematics
- Topic: does every unit length curve lie inside the semicircle?
- Replies:
**12** - Views:
**3262**

### Re: does every unit length curve lie inside the semicircle?

Building off of Madaco's idea... Any unit length curve that won't fit can be placed in such a way so that the length that does fall inside the circle is maximized. Let's call it the "maximal contained curve" (MCC). To make things easier, let me define a semicircle: The semicircle is center...

- Fri Mar 11, 2016 4:06 am UTC
- Forum: Serious Business
- Topic: Ethics of Suicidal Action
- Replies:
**12** - Views:
**6178**

### Re: Ethics of Suicidal Action

I would argue any discussion of this subject will either result in something equivalent to "God says so" or something to do with emotional attachment. You know I take the former opinion, and you obviously take the latter. It would probably make me sad, but there isn't an ethical issue invo...

- Fri Mar 11, 2016 3:48 am UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**3200**

### Re: Three Water Tanks

Can there wind up being a non-integer amount of water in any given tank? For example, if the capacity was 40 liters, and first you request 15 liters from tank A, so the division is 25:40:40, and then an hour later you request 40 liters from tank A. Would it fill up so that the ratio is 40:32.5:32.5...

- Thu Mar 10, 2016 8:37 pm UTC
- Forum: Serious Business
- Topic: Ethics of Suicidal Action
- Replies:
**12** - Views:
**6178**

### Re: Ethics of Suicidal Action

For the same reason they care about things knowing that they will die one day anyway. Nihilism (as a personal philosophy) is not a natural and inevitable consequence of a finite lifespan, nor of the heat death of the universe. Sure, but that's not logical. It's based on personal preference. So in t...

- Thu Mar 10, 2016 7:50 pm UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**3200**

### Re: Three Water Tanks

Sorry the wording wasn't clear. I thought a word problem would be more interesting. I have added a more abstract version to the OP.

- Wed Mar 09, 2016 8:57 pm UTC
- Forum: Logic Puzzles
- Topic: Three Water Tanks
- Replies:
**7** - Views:
**3200**

### Three Water Tanks

There are three perfectly identical water tanks arranged so that each tank is equidistant from the other two. The tanks are interconnected with a pipe system, and each tank is filled to its maximum capacity with water. Your goal is to figure out the maximum capacity. You know the volume of each tank...

- Tue Mar 08, 2016 5:39 pm UTC
- Forum: Science
- Topic: Relativistic Lorentz force
- Replies:
**34** - Views:
**5939**

### Re: Relativistic Lorentz force

Hypnosifl, your explanation was really helpful. I think the crucial thing is to not consider the magnetic field as its own entity, but rather as a phenomenon produced by moving charges. The particular movement of those charges become distorted when you change reference frames.

- Mon Mar 07, 2016 10:32 pm UTC
- Forum: Science
- Topic: Relativistic Lorentz force
- Replies:
**34** - Views:
**5939**

### Re: Relativistic Lorentz force

SuicideJunkie wrote:Is this the "A moving magnetic field looks like an electric field" thing?

Probably, but why? The magnetic field at (0,0,0) and the magnetic field at (0,dy,0) are identical. How does it magically become electric field if the field isn't changing?

- Mon Mar 07, 2016 8:25 pm UTC
- Forum: Serious Business
- Topic: Ethics of Suicidal Action
- Replies:
**12** - Views:
**6178**

### Re: Ethics of Suicidal Action

At the end of the day morality pretty much goes out the window when it comes to suicide. For many people, at least on this forum, death means oblivion. Why would someone care about the morality of suicide if they are seeking to leave every aspect of humanity behind? It's like saying "should esc...

- Mon Mar 07, 2016 8:05 pm UTC
- Forum: Science
- Topic: Relativistic Lorentz force
- Replies:
**34** - Views:
**5939**

### Relativistic Lorentz force

I feel like this is a stupid question, but I'm blanking on the justification for why the Lorentz force makes sense in terms of special relativity. Please note that I am well aware there exist mathematical formalism for this. I'm looking for a more conceptual explanation. Suppose you have a positive ...

- Fri Mar 04, 2016 9:04 am UTC
- Forum: Logic Puzzles
- Topic: Optimize tiling for a 50x50 grid
- Replies:
**7** - Views:
**3102**

### Re: Optimize tiling for a 50x50 grid

Impressive Jaap!

I only managed to get one with 17 squares left with graph paper. I didn't think it was possible to fill all 2500. If you ran a computer algorithm, do you mind sharing the code?

I only managed to get one with 17 squares left with graph paper. I didn't think it was possible to fill all 2500. If you ran a computer algorithm, do you mind sharing the code?

- Thu Mar 03, 2016 9:08 pm UTC
- Forum: Logic Puzzles
- Topic: Optimize tiling for a 50x50 grid
- Replies:
**7** - Views:
**3102**

### Re: Optimize tiling for a 50x50 grid

jaap wrote:Cradarc wrote:3. A M x N tile placed on the grid will give you P = NM - 0.5*(N+M) points (ie. area - semiperimeter)

That's not the semiperimeter, it's a quarter of the perimeter.

Sorry, brain fart. It should be fixed now.

- Wed Mar 02, 2016 11:14 pm UTC
- Forum: Logic Puzzles
- Topic: Optimize tiling for a 50x50 grid
- Replies:
**7** - Views:
**3102**

### Optimize tiling for a 50x50 grid

You are given a rectangular grid with dimensions 50 x 50 and a supply of rectangular tiles of various sizes. Your goal is to earn as many points as possible by placing tiles on the grid. Rules: 1. Tiles cannot overlap or extend outside the grid. 2. Tiles must line up with the grid lines, so they can...

- Fri Feb 26, 2016 3:19 am UTC
- Forum: Mathematics
- Topic: Is math real?
- Replies:
**105** - Views:
**15044**

### Re: Is math real?

Just because the human mind really wants nature to make sense, doesn't mean that the universe is obliged to cater our whims. Yet, somehow, when we try to use logical abstract concepts to make sense of nature, it works . It has nothing to do with how much we want something to be true. It has to do w...

- Thu Feb 25, 2016 10:53 pm UTC
- Forum: Mathematics
- Topic: Is math real?
- Replies:
**105** - Views:
**15044**

### Re: Is math real?

Is logic real? Math is just structured logic and abstracted objects. The fact that equations can explain physical phenomena is more about the human mind than it is about nature. There are no equations in nature, but we perceive them there because it makes more sense to us. It allows us to generalize...

- Sun Feb 21, 2016 11:25 pm UTC
- Forum: Logic Puzzles
- Topic: Two gold nugget puzzle
- Replies:
**17** - Views:
**4372**

### Re: Two gold nugget puzzle

Good catch, PeteP. I misunderstood the problem.

In that case, the minimum value should be around O(n) = ~16 since you're basically creating a max heap out of an unsorted array. (After you have the heap, it is trivial to remove the two highest elements).

In that case, the minimum value should be around O(n) = ~16 since you're basically creating a max heap out of an unsorted array. (After you have the heap, it is trivial to remove the two highest elements).

- Sun Feb 21, 2016 8:30 pm UTC
- Forum: Logic Puzzles
- Topic: Two gold nugget puzzle
- Replies:
**17** - Views:
**4372**

### Re: Two gold nugget puzzle

Note theoretical minimum number of weighings is 5. 16 choose 2 = 120. Each weighing can give 3 distinct results. Logbase3(120) = ~4.36 Weight half of the nuggets against the other half. - If both halves are equal, then perform the heavy coin method on each half. - If one half is heavier, remove the ...

- Sun Feb 21, 2016 8:39 am UTC
- Forum: Mathematics
- Topic: "super" binary number system
- Replies:
**4** - Views:
**1855**

### Re: "super" binary number system

Thanks Chridd. It handles the duplicate representations in the way I want. The only issue I have is the subtraction part. That looks costly because it requires converting the digit in question into a binary value. I don't really see the point of replacing k bits ahead by a digit with 2^k+2 values. T...

- Sat Feb 20, 2016 10:07 pm UTC
- Forum: Mathematics
- Topic: "super" binary number system
- Replies:
**4** - Views:
**1855**

### "super" binary number system

I've been musing about a particular numbering system which may already exist (if it does, please link me to info!). It's very similar to binary except that the nth digit can take on n+1 different values instead of just two. I will only be working with integers, but perhaps it can be expanded into ra...

- Fri Feb 19, 2016 7:40 am UTC
- Forum: Forum Games
- Topic: Duties and Obligations
- Replies:
**2** - Views:
**562**

### Duties and Obligations

Summary The community will build up a List of Duties. "Duties" are simply things that must appear in posts which satisfy a criterion. Every post must perform all applicable duties given in the list. Some examples: - Prime-numbered posts must contain a cat picture. - Posts with numbers tha...

- Wed Feb 17, 2016 9:03 pm UTC
- Forum: Serious Business
- Topic: Education requirements for elected officials
- Replies:
**70** - Views:
**14082**

### Re: Education requirements for elected officials

@Elasto If you look more into the background of Mujica, you will notice he was very active in politics before being elected into office. At the time of his election, he was not a mere farmer. He was well acquainted with the world of politics. In my OP, I explicitly stated formal education is not req...

- Wed Feb 17, 2016 4:45 am UTC
- Forum: Serious Business
- Topic: Education requirements for elected officials
- Replies:
**70** - Views:
**14082**

### Re: Education requirements for elected officials

Under what circumstances will a stereotypical farm hand be more qualified to be president than a stereotypical professor of Constitutional law? Statistically speaking, they are both equally likely to become corrupted by power. The farm hand, however, will be more easily manipulated due to his naivet...

- Tue Feb 16, 2016 2:39 am UTC
- Forum: Serious Business
- Topic: Education requirements for elected officials
- Replies:
**70** - Views:
**14082**

### Re: Education requirements for elected officials

Some good points made. Is there any evidence that legislators with law degrees are actually better? And, even if there was, do we really want a system where our lawmakers all come from essentially the same background? Some would argue that having different backgrounds and areas of expertise is actua...

- Mon Feb 15, 2016 7:15 pm UTC
- Forum: Serious Business
- Topic: Education requirements for elected officials
- Replies:
**70** - Views:
**14082**

### Education requirements for elected officials

NOTE: I live in the U.S.A so that's the political environment I'm drawing my experience from. Feel free to to discuss other countries though. Politics in the modern world is ridiculously complex. Clearly there are some people who are simply not qualified to hold certain positions in the government. ...

- Sat Feb 06, 2016 2:57 am UTC
- Forum: Logic Puzzles
- Topic: Six roll dice game
- Replies:
**11** - Views:
**3171**

### Re: Six roll dice game

I think Jeff's answer makes sense. The rolls are independent so it doesn't matter if you rolled 0 times or 5 times before. The fact of the matter is you have a total of six trials to get a desirable value. The probability of there being at least one 6 is: P 6 = 1-(5/6)^6 = ~0.6651 The pr...

- Fri Feb 05, 2016 10:26 am UTC
- Forum: Mathematics
- Topic: Infinite balls
- Replies:
**6** - Views:
**2097**

### Re: Infinite balls

I don't think it's a paradox. Fact 1: The number of balls in the room grows without bound with successive steps. Fact 2: Every ball placed in the room during any given step will be taken out in another future step. These two facts do not contradict because the number of steps are NOT finite. If you'...