## Search found 2081 matches

- Fri Jan 15, 2016 5:48 pm UTC
- Forum: Logic Puzzles
- Topic: A question about stacking dominoes
- Replies:
**5** - Views:
**2151**

### Re: A question about stacking dominoes

So you need atleast 2x dominoes to support x dominoes. Anyway let's start building in the reverse direction, if you can add a valid layer below a layer you could have done it the other way around. I assume that adding dominoes to the layer below that don't support any stone does not improve...

- Fri Jan 15, 2016 5:35 pm UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**19729**

### Re: Unusual Cake Slicing

Here is a dissection I found that I believe to be new, which is completely unrelated to any of the ones in this thread or in the paper.

Edit:

Colin Wright pointed out that this is an extreme case of the infinite family in the paper:

Edit:

Colin Wright pointed out that this is an extreme case of the infinite family in the paper:

- Fri Jan 15, 2016 3:49 pm UTC
- Forum: Logic Puzzles
- Topic: A question about stacking dominoes
- Replies:
**5** - Views:
**2151**

### A question about stacking dominoes

Here's a neat question someone asked me when he was developing a two-player game. Suppose you have a large number of identical 2x1 tiles, i.e. dominoes, and a large board with a square grid of the same size as the dominoes. You can place the dominoes on the board, but must follow these rules: ⋅...

- Thu Jan 14, 2016 7:06 am UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**19729**

### Re: Unusual Cake Slicing

One year later, gizmodo catches up. http://gizmodo.com/mathematicians-have-found-crazy-new-ways-to-cut-pizza-i-1751776752 The paper was put on arxiv a month ago. It is doing the rounds now because New Scientist published an article about it last week. While the paper is from last year, I would not ...

- Wed Jan 13, 2016 6:40 pm UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**19729**

### Re: Unusual Cake Slicing

There has been a new development: http://arxiv.org/pdf/1512.03794.pdf This paper shows some interesting new dissections of the circle into equal parts, not all on the boundary. It even references this thread. Still no solutions where the centre falls inside a piece, though. See also: http://www.ifls...

- Tue Jan 05, 2016 9:03 am UTC
- Forum: Movies and TV Shows
- Topic: Star Wars: Episode 7: Electric Boogaleven
- Replies:
**479** - Views:
**112764**

### Re: Star Wars: Episode 7: Electric Boogaleven

There's something in this movie's final fight that I'm sure I have seen before in some other film, but I can't think which one, namely the way Kylo Ren thumps his wounded side, as if to keep his body working Does anyone know where this was done before? Edit: I think it could be from a samurai movie,...

- Tue Jan 05, 2016 8:53 am UTC
- Forum: Logic Puzzles
- Topic: Blue Eyes with Superrationality
- Replies:
**48** - Views:
**10408**

### Re: Blue Eyes with Superrationality

Even though they all can agree that there is at least one blue-eyed person on the island, they don't mean the same thing when they say that. It really means, "amongst the N-1 people that are not me, there is at least one blue-eyed person". That statement is self-referential, and refers to ...

- Thu Dec 31, 2015 6:50 am UTC
- Forum: Logic Puzzles
- Topic: Probability of ending up in room N
- Replies:
**3** - Views:
**2250**

### Re: Probability of ending up in room N

Not really. You also have an infinite number of rounds to play, and each round has a non-zero chance of success. While it is theoretically possible to lose an infinite number of times, the probability of that happening is zero. You are almost surely going to win some round. What about this scenario...

- Wed Dec 30, 2015 10:27 am UTC
- Forum: Logic Puzzles
- Topic: Probability of ending up in room N
- Replies:
**3** - Views:
**2250**

### Re: Probability of ending up in room N

I've just "dreamt" this up, so if it's unsolvable (or even too easy) .... go easy on me please :) So you check into a plush hotel and pay your $40 for 1 night's stay. You are then told you've been allocated room 1 (which is a bit of a bummer. as the rooms get better as the room number inc...

- Tue Dec 29, 2015 12:14 am UTC
- Forum: Logic Puzzles
- Topic: Escape the bear in the circle?
- Replies:
**22** - Views:
**5898**

### Re: Escape the bear in the circle?

This is because your strategy would push the person closer and closer to the boundary. Even while moving in a circle, the bear can position itself to force the tangential direction of the prey's circular path to move towards the boundary. The tangential direction of the person's path, by definition...

- Sun Dec 27, 2015 9:02 am UTC
- Forum: Logic Puzzles
- Topic: Escape the bear in the circle?
- Replies:
**22** - Views:
**5898**

### Re: Escape the bear in the circle?

The explanations Notzeb linked to are suspiciously like the Zeno's paradox. At every step, the lion/bear gets closer to the person, yet it never fully overlap the person. Basically, the bear can get arbitrarily close, but never actually reach its prey. I agree that the proof in that paper there is ...

- Mon Nov 30, 2015 12:26 pm UTC
- Forum: Movies and TV Shows
- Topic: Doctor Whom
- Replies:
**4990** - Views:
**723742**

- Tue Nov 24, 2015 2:35 pm UTC
- Forum: Coding
- Topic: [Answered] Basic question about storing function results
- Replies:
**3** - Views:
**3288**

- Tue Nov 24, 2015 11:47 am UTC
- Forum: Mathematics
- Topic: Least numbers discarded when dealing cards
- Replies:
**30** - Views:
**6348**

### Re: Least numbers discarded when dealing cards

Do you understand what my method does? No, I have no idea what s % n function does. That is the 'mod' operator, and s%n means the remainder when dividing s by n. So 1000%52 = 12 because 1000=19*52+12. Perhaps if I add 52 to 52 until I find a number 100...00 it could be used in base 52. Though I'd s...

- Fri Nov 20, 2015 10:54 am UTC
- Forum: Mathematics
- Topic: Least numbers discarded when dealing cards
- Replies:
**30** - Views:
**6348**

### Re: Least numbers discarded when dealing cards

Am I missing something or are people way overthinking this? Just put the numbers 1 through 52 in an array and shuffle it. Dealing cards is as simple as pulling out elements starting from the first index and working your way down. The problem is that in step 2 of that shuffling algorithm you need to...

- Wed Nov 18, 2015 3:44 pm UTC
- Forum: Logic Puzzles
- Topic: Find the Mole
- Replies:
**5** - Views:
**2306**

### Re: Find the Mole

This is a repeat of:

viewtopic.php?f=3&t=62767

viewtopic.php?f=3&t=62767

- Mon Nov 16, 2015 9:33 pm UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9944** - Views:
**1910825**

### Re: Coding: Fleeting Thoughts

This discussion of for reminds me of this beautiful yet ghastly construct:

Code: Select all

`for(unsigned i = 10; i --> 0;)`

{

//stuff

}

- Thu Nov 12, 2015 9:31 am UTC
- Forum: Computer Science
- Topic: Reconstructing a tiling from "is-adjacent-to" data?
- Replies:
**10** - Views:
**7982**

### Re: Reconstructing a tiling from "is-adjacent-to" data?

By the way, the solution is usually not unique. For example, if you have 4 countries where each is adjacent to all three others, then you can draw a map in 8 distinct ways: You can choose any of the 4 countries to be in the middle, landlocked by the other three countries, and those other three can b...

- Wed Nov 11, 2015 11:16 am UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**58600**

### Re: Escape the Frictionless Circle

There is a loophole in the puzzle wording: A perfectly flat plane does not necessarily have to be perfectly level. If it's a sloping flat plane, you will automatically reach the outside of the circle. I also thought about what it means to have a perfectly flat surface on a round earth. Unfortuna...

- Tue Nov 10, 2015 6:23 pm UTC
- Forum: Computer Science
- Topic: Reconstructing a tiling from "is-adjacent-to" data?
- Replies:
**10** - Views:
**7982**

### Re: Reconstructing a tiling from "is-adjacent-to" data?

You can think of this data as a graph, where the countries are vertices and the 'is adjacent to' relation gives you the edges. Your question then boils down to this: Given a planar graph, draw it without any crossing edges. Or in more mathematical terms, find an embedding of a planar graph in the pl...

- Mon Nov 09, 2015 4:21 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**58600**

### Re: Escape the Frictionless Circle

I wasn't clear there, I meant it wouldn't work for this puzzle's situation, not for a ball situation. If the floor can't distort here and the normal forces are all purely vertical, I don't see how the CoM of the system (gold block + person) can be shifted laterally. Sorry, for misunderstanding you....

- Mon Nov 09, 2015 3:08 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**58600**

### Re: Escape the Frictionless Circle

The first thing that comes to mind is the answer to a problem that I read at some point: If a ball is rolling on an infinite, perfectly flat, surface, in a vacuum, will it ever stop? The answer was yes, because the ball exerts more force on the surface in the direction it is traveling in than the o...

- Fri Nov 06, 2015 5:28 pm UTC
- Forum: Logic Puzzles
- Topic: Timed Bridge Problem
- Replies:
**3** - Views:
**2034**

- Fri Nov 06, 2015 1:12 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**156** - Views:
**58600**

### Re: Escape the Frictionless Circle

I thought for a moment that you could do this: Give the gold block some spin. Assuming you are a foot or two away from the gold block rather than directly on top of it, this will push you around the block in the opposite direction, so as soon as you let go of the block you will be moving away in a s...

- Wed Oct 28, 2015 6:01 pm UTC
- Forum: Mathematics
- Topic: Euler totient and powers of 2 minus 1
- Replies:
**10** - Views:
**2280**

### Re: Euler totient and powers of 2 minus 1

I was too slow, but here is my proof anyway: Start with Euler's Theorem , which says that a phi(m) = 1 mod m for any coprime integers a and m. For our purposes we choose a=2, and m=2 n -1, which are obviously coprime. So 2 phi(m) = 1 mod 2 n -1. The multiplicative order of 2 in the g...

- Mon Oct 26, 2015 1:39 pm UTC
- Forum: Mathematics
- Topic: Combinatorics : counting problem
- Replies:
**7** - Views:
**1812**

### Re: Combinatorics : counting problem

If I did not make a mistake I have found only 4 permutations repeating themselves : 2,3,4,5,6 6,5,2,3,4 4,3,2,5,6 6,5,4,3,2 The starting numbers are : 2,24,32,54,62,84,92,..... 2+22=24 24+8=32 32+22=54 54+8=62 62+22=84 84+8=92 Alternatively we add 22 and after 22 we add 8 and so on I do not know if...

- Thu Oct 15, 2015 12:50 pm UTC
- Forum: Movies and TV Shows
- Topic: Do you enjoy car chase scenes in movies?
- Replies:
**19** - Views:
**5728**

### Re: Do you enjoy car chase scenes in movies?

The classic Bullitt car chase scene has become a bit cheesy for me when it was pointed out that

I can't help but notice that now and, while still fun, that makes it cheesy fun instead of exciting fun.

**Spoiler:**

- Wed Oct 14, 2015 2:29 pm UTC
- Forum: Movies and TV Shows
- Topic: Do you enjoy car chase scenes in movies?
- Replies:
**19** - Views:
**5728**

### Re: Do you enjoy car chase scenes in movies?

One of the cool things about Fury Road was just that it was all real, actual stunts (even if the action happened to be sped up at some point in production). They thought they might have to use CGI for safety reasons, but I think pretty much everything (aside from the speed) was actually done -- the...

- Tue Oct 13, 2015 5:25 pm UTC
- Forum: Mathematics
- Topic: Congruences
- Replies:
**1** - Views:
**1266**

### Re: Congruences

Hi, While trying to solve a problem linked to a primality test I encountered another one. Here is my problem. I did some tests it works. n=2k+1 k>0 a=(2^(2k+1))-1 b=(2^(10k+5)-1) c=(2^(10k+5)+1) Show that either b = 0 mod a either c= 0 mod a Thank you for any clue. x 5 -1 = (x-1)(x 4 +x 3 +x 2 +x+1...

- Fri Oct 09, 2015 12:13 pm UTC
- Forum: Logic Puzzles
- Topic: Kirkman's Schoolgirls
- Replies:
**12** - Views:
**3807**

### Re: Kirkman's Schoolgirls

I think I have a solution. 05A 06C 07E 0B7 0C9 D08 E09 16B 17D 18A 1C8 1D5 E19 A15 27C 28E 29B 2D9 2E6 A25 B26 38D 39A 35C 3E5 3A7 B36 C37 49E 45B 46D 4A6 4B8 C47 D48 Note that 'abreast' in the original problem does not necessarily mean adjacent in a triplet. What is meant is that no pair of school...

- Thu Oct 08, 2015 5:25 am UTC
- Forum: Logic Puzzles
- Topic: Timed Bridge Problem
- Replies:
**5** - Views:
**3556**

### Re: Timed Bridge Problem

If Adam is responsible for holding the lantern the entire time, you get AD A AC A AB, for 2A + B + C + D. This could be faster, or it could not--the specific times aren't given, so we have no way of knowing whether 2B is faster or slower than A+C. We would need to know this in order to determin...

- Mon Oct 05, 2015 1:48 pm UTC
- Forum: Mathematics
- Topic: Solving diophantine equation
- Replies:
**5** - Views:
**1186**

### Re: Solving diophantine equation

Hi, Here is a polynomial P(k) P(k)=2*(a+k)!-k^2-k(2b+1)-b+6 where a and b are positive integers >0 Assuming that P(k) could be negative for some (k0,a,b) and positive for some (k1,a,b) can we state or claim that P(k)=0 has at least one solution. Thank you for your thoughts. No. Firstly, P(k) is not...

- Fri Oct 02, 2015 10:39 pm UTC
- Forum: Logic Puzzles
- Topic: Caesar cipher
- Replies:
**3** - Views:
**2214**

### Re: Caesar cipher

**Spoiler:**

- Fri Oct 02, 2015 12:30 pm UTC
- Forum: Logic Puzzles
- Topic: How many rooms are there in the tower?
- Replies:
**26** - Views:
**5630**

### Re: How many rooms are there in the tower?

This reminds me of a technique I used to use occasionally in a painting program. If there was an area that had been dithered (i.e. was coloured in some pattern using two distinct colours) and I wanted it to be just one colour, I would alternate floodfilling it with one colour and then the o...

- Wed Sep 30, 2015 9:17 am UTC
- Forum: Science
- Topic: Speed of waves in water
- Replies:
**8** - Views:
**5505**

### Re: Speed of waves in water

Googling gave me this site that has an idealised formula: http://hyperphysics.phy-astr.gsu.edu/hbase/watwav.html#c3 This says that for deep water, wave speed becomes proportional to sqrt(wavelength), but for shallow water the speed becomes independent of wavelength. So, water waves do travel at dif...

- Tue Sep 29, 2015 11:26 am UTC
- Forum: Science
- Topic: Speed of waves in water
- Replies:
**8** - Views:
**5505**

### Re: Speed of waves in water

Googling gave me this site that has an idealised formula:

http://hyperphysics.phy-astr.gsu.edu/hb ... av.html#c3

This says that for deep water, wave speed becomes proportional to sqrt(wavelength), but for shallow water the speed becomes independent of wavelength.

http://hyperphysics.phy-astr.gsu.edu/hb ... av.html#c3

This says that for deep water, wave speed becomes proportional to sqrt(wavelength), but for shallow water the speed becomes independent of wavelength.

- Mon Sep 28, 2015 7:00 am UTC
- Forum: Mathematics
- Topic: Theoretical problem about traveler salesman
- Replies:
**6** - Views:
**1989**

### Re: Theoretical problem about traveler salesman

The problem doesn't get much easier when you know the exact length of the shortest path ahead of time. You can prove this by imagining you had a magic box (aka oracle) which could solve the problem if it was told ahead of time the exact length of the shortest path, and then use the magic box to sol...

- Wed Sep 23, 2015 5:24 pm UTC
- Forum: Mathematics
- Topic: geometry [looking at triangles in perspective]
- Replies:
**7** - Views:
**1960**

### Re: geometry [looking at triangles in perspective]

It does seem to be a bit tricky. but you've got a sound argument. Actually, I don't. For obtuse triangles my argument does not work, because my #2 should have read "the intersection of any two of the spheres must not lie wholly within the third". For this case you do need to use a smaller...

- Wed Sep 23, 2015 2:54 pm UTC
- Forum: Mathematics
- Topic: geometry [looking at triangles in perspective]
- Replies:
**7** - Views:
**1960**

### Re: geometry [looking at triangles in perspective]

It does seem to be a bit tricky. I think you can simplify things by choosing 90 degrees as your viewing angle, i.e. try to find point P such that angles APB, BPC, CPA are all 90 degrees. The points in 3d space such that angle APB is 90 degrees is exactly the sphere that has AB as its diameter. The s...

- Fri Sep 11, 2015 10:01 am UTC
- Forum: Mathematics
- Topic: I don't seem to understand my own brain teaser, please help!
- Replies:
**22** - Views:
**4991**

### Re: I don't seem to understand my own brain teaser, please h

The expected value is positive because you can never lose more than 10 days but if you win you can win high. Exactly. Even just playing twice, you have: 0.55^2 = 30.25% probability of getting 4 times your initial amount 2*0.55*0.45 = 49.5% probability of getting 0.6 times your initial amount 0.45^2...