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by jaap
Thu Feb 18, 2016 8:18 pm UTC
Forum: Logic Puzzles
Topic: Simple maths problem?
Replies: 9
Views: 2548

Re: Simple maths problem?

((1+2)/3)^4 * 5 +6 +7 -8 -9


Edited to add extra pair of brackets.
by jaap
Thu Feb 18, 2016 8:07 pm UTC
Forum: Logic Puzzles
Topic: Simple maths problem?
Replies: 9
Views: 2548

Re: Simple maths problem?

Isn't that rather easy?
1+2+3+4-5+6+7-8-9
1-2-3+4+5+6+7-8-9
1+2+3+4+5-6-7+8-9
1+2-3-4+5-6+7+8-9
by jaap
Mon Feb 15, 2016 5:39 pm UTC
Forum: Mathematics
Topic: Combinatorics : Castle, rooms and doors
Replies: 14
Views: 2647

Re: Combinatorics : Castle, rooms and doors

If we find a general formula for nxn with 0,1,2,3,4 doors then we wil obtain 2 doors by substraction. Subtraction from what? The number of nxn configurations where all the rooms have the same number of doors? How will that be calculated? Anyway, here are the results that I got by computer: x 1 2 3 ...
by jaap
Sun Feb 14, 2016 11:15 am UTC
Forum: Mathematics
Topic: Combinatorics : Castle, rooms and doors
Replies: 14
Views: 2647

Re: Combinatorics : Castle, rooms and doors

I get 86 for 2x2. Starting from 54 for the 3-room"L", 11 have two open doors towards the fourth room (->11 options), 11 have no open door (->11 options), and 32 have one open door (->2*32 options), for a total of 86 options. Finding that number of 11 was not trivial, so I don't see an eas...
by jaap
Fri Feb 12, 2016 4:05 pm UTC
Forum: Mathematics
Topic: Cardinality of subset of the powerset of naturals
Replies: 5
Views: 1468

Re: Cardinality of subset of the powerset of naturals

But for c = 0, isn't there still no natural number k which describes the size of infinite elements of S? Yet, since there is only one set in S of size |k| for each k in N (because k^c = 1), S is now countable. To restate what arbiteroftruth is getting at: Your statement "for all k in N, there ...
by jaap
Tue Feb 09, 2016 1:16 pm UTC
Forum: Logic Puzzles
Topic: A question about stacking spheres
Replies: 2
Views: 1933

Re: A question about stacking spheres

I assume you can't just remove spheres again? Yes, that is what I meant but didn't actually specify. Let's see the bottom layer can only have a even number sticking up, and the 3x3 layer only an uneven number and if an uneven number is alredy occupied on the 2x2 layer then everything is fine. B...
by jaap
Tue Feb 09, 2016 10:36 am UTC
Forum: Logic Puzzles
Topic: A question about stacking spheres
Replies: 2
Views: 1933

A question about stacking spheres

From the same person who asked me a question about stacking dominoes , here is a question about stacking spheres. Suppose you want to build a square pyramid made up of 30 spheres. So the bottom layer is a 4x4 arrangement of touching spheres, and it has 3x3, 2x2 and 1x1 layers on top. The building bl...
by jaap
Mon Feb 08, 2016 4:15 pm UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1438

Re: Coin flip problem

With that you should be able to follow the rest of Cauchy's post that transforms that second term, the probability of a sequence that reaches m but ends below it, into the probability of a sequence that ends above m. I appreciate that you assumed I was the one explaining, but it just ain't so. Cred...
by jaap
Mon Feb 08, 2016 9:25 am UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1438

Re: Coin flip problem

This is a trick I learned once for the "drunkard's walk" formulation. Let X k equal the number of heads minus the number of tails after k tosses. The probability that X k stays below m forever is equal to P(X n < m) - P(X n < m and X k = m for some k). For each sequence of flips in the la...
by jaap
Thu Feb 04, 2016 1:21 am UTC
Forum: Movies and TV Shows
Topic: Star Wars: Episode 7: Electric Boogaleven
Replies: 479
Views: 101336

Re: Star Wars: Episode 7: Electric Boogaleven

Well Cloverfield clearly hasn't vanished down the memory hole yet if you're mentioning it... People know it existed, sure. But nobody cares about it. Nobody thinks back and says "man, you know what was a good movie?" In twenty years, people won't even remember it was a thing unless they s...
by jaap
Fri Jan 15, 2016 5:48 pm UTC
Forum: Logic Puzzles
Topic: A question about stacking dominoes
Replies: 5
Views: 1902

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...
by jaap
Fri Jan 15, 2016 5:35 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 17554

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.
circledissection.gif
circledissection.gif (1.77 KiB) Viewed 1339 times


Edit:
Colin Wright pointed out that this is an extreme case of the infinite family in the paper:
circledissection2.png
by jaap
Fri Jan 15, 2016 3:49 pm UTC
Forum: Logic Puzzles
Topic: A question about stacking dominoes
Replies: 5
Views: 1902

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: ⋅...
by jaap
Thu Jan 14, 2016 7:06 am UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 17554

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 ...
by jaap
Wed Jan 13, 2016 6:40 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 17554

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...
by jaap
Tue Jan 05, 2016 9:03 am UTC
Forum: Movies and TV Shows
Topic: Star Wars: Episode 7: Electric Boogaleven
Replies: 479
Views: 101336

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,...
by jaap
Tue Jan 05, 2016 8:53 am UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 9156

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 ...
by jaap
Thu Dec 31, 2015 6:50 am UTC
Forum: Logic Puzzles
Topic: Probability of ending up in room N
Replies: 3
Views: 1935

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...
by jaap
Wed Dec 30, 2015 10:27 am UTC
Forum: Logic Puzzles
Topic: Probability of ending up in room N
Replies: 3
Views: 1935

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...
by jaap
Tue Dec 29, 2015 12:14 am UTC
Forum: Logic Puzzles
Topic: Escape the bear in the circle?
Replies: 22
Views: 4857

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...
by jaap
Sun Dec 27, 2015 9:02 am UTC
Forum: Logic Puzzles
Topic: Escape the bear in the circle?
Replies: 22
Views: 4857

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 ...
by jaap
Mon Nov 30, 2015 12:26 pm UTC
Forum: Movies and TV Shows
Topic: Doctor Whom
Replies: 4906
Views: 579176

Re: Doctor Whom

by jaap
Tue Nov 24, 2015 11:47 am UTC
Forum: Mathematics
Topic: Least numbers discarded when dealing cards
Replies: 30
Views: 5453

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...
by jaap
Fri Nov 20, 2015 10:54 am UTC
Forum: Mathematics
Topic: Least numbers discarded when dealing cards
Replies: 30
Views: 5453

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...
by jaap
Wed Nov 18, 2015 3:44 pm UTC
Forum: Logic Puzzles
Topic: Find the Mole
Replies: 5
Views: 2025

Re: Find the Mole

This is a repeat of:
viewtopic.php?f=3&t=62767
by jaap
Mon Nov 16, 2015 9:33 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9775
Views: 1602433

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
}
by jaap
Thu Nov 12, 2015 9:31 am UTC
Forum: Computer Science
Topic: Reconstructing a tiling from "is-adjacent-to" data?
Replies: 10
Views: 6779

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...
by jaap
Wed Nov 11, 2015 11:16 am UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 156
Views: 36711

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...
by jaap
Tue Nov 10, 2015 6:23 pm UTC
Forum: Computer Science
Topic: Reconstructing a tiling from "is-adjacent-to" data?
Replies: 10
Views: 6779

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...
by jaap
Mon Nov 09, 2015 4:21 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 156
Views: 36711

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....
by jaap
Mon Nov 09, 2015 3:08 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 156
Views: 36711

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...
by jaap
Fri Nov 06, 2015 5:28 pm UTC
Forum: Logic Puzzles
Topic: Timed Bridge Problem
Replies: 3
Views: 1789

Re: Timed Bridge Problem

by jaap
Fri Nov 06, 2015 1:12 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 156
Views: 36711

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...
by jaap
Wed Oct 28, 2015 6:01 pm UTC
Forum: Mathematics
Topic: Euler totient and powers of 2 minus 1
Replies: 10
Views: 1931

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...
by jaap
Mon Oct 26, 2015 1:39 pm UTC
Forum: Mathematics
Topic: Combinatorics : counting problem
Replies: 7
Views: 1722

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...
by jaap
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: 4931

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
Spoiler:
there's this VW Beetle that appears in every other shot, and the cars lose more than 4 hubcaps
I can't help but notice that now and, while still fun, that makes it cheesy fun instead of exciting fun.
by jaap
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: 4931

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...
by jaap
Tue Oct 13, 2015 5:25 pm UTC
Forum: Mathematics
Topic: Congruences
Replies: 1
Views: 1202

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...
by jaap
Fri Oct 09, 2015 12:13 pm UTC
Forum: Logic Puzzles
Topic: Kirkman's Schoolgirls
Replies: 12
Views: 3174

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...

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