Search found 2067 matches

Fri Nov 20, 2015 10:54 am UTC
Forum: Mathematics
Topic: Least numbers discarded when dealing cards
Replies: 30
Views: 5794

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: 2131

Re: Find the Mole

This is a repeat of:
viewtopic.php?f=3&t=62767
Mon Nov 16, 2015 9:33 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9848
Views: 1732592

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: 7488

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: 45009

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: 7488

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: 45009

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: 45009

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: 1880

Re: Timed Bridge Problem

Fri Nov 06, 2015 1:12 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 156
Views: 45009

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: 2137

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: 1759

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: 5313

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.
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: 5313

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: 1241

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: 3464

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: 3320

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: 1133

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: 2049

Re: Caesar cipher

Spoiler:
ONE OF TGHE OLDEST CIPHERS IS CALLED A
CAESAR CIPHER WHICH WAS DESCRIBED BY
IULIUS CAESAR IN HIS NOTES ABOUT THE WAR
IN GAUL
Fri Oct 02, 2015 12:30 pm UTC
Forum: Logic Puzzles
Topic: How many rooms are there in the tower?
Replies: 26
Views: 5111

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: 4730

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: 4730

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.
Mon Sep 28, 2015 7:00 am UTC
Forum: Mathematics
Topic: Theoretical problem about traveler salesman
Replies: 6
Views: 1884

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: 1854

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: 1854

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
Replies: 22
Views: 4762

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...
Wed Sep 09, 2015 8:52 am UTC
Forum: Logic Puzzles
Topic: Fill square puzzle
Replies: 4
Views: 1941

Re: Fill square puzzle

The intended answer is of course:
Spoiler:

Code: Select all

`....*.*.....*...*........`

XYZ
Thu Aug 27, 2015 3:29 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9848
Views: 1732592

Re: Coding: Fleeting Thoughts

Open that in Chrome, or IE, you get a text box with some words after it. But open it in Firefox, and you just get an ellipsis. Except the text box is still there - mouse over where it should be and you get the text-edit cursor, and click and it'll focus the text box, which will suddenly appear agai...
Fri Aug 21, 2015 6:11 am UTC
Forum: Language/Linguistics
Topic: ei <-> ie: English speciality?
Replies: 24
Views: 6521

Re: ei <-> ie: English speciality?

Derek wrote:
gmalivuk wrote:For me at least, weird definitely rhymes with tiered.

I agree, and stand by my original question?

Weird rhymes with tiered/feared, but this is not the same sound as feel/receive/protein.
Just like peer and peel have different sounds.
(For me at least - I have a BrE accent.)
Thu Aug 20, 2015 9:16 am UTC
Forum: Logic Puzzles
Topic: Three Cards Trick
Replies: 15
Views: 2677

Re: Three Cards Trick

I have read of a legitimate variant of this trick, but that involved 5 cards: - 5 cards are freely chosen from a deck of 52. - The Magician's assistant chooses one of these 5 cards, and lays the other 4 face up in a row. - Those 4 cards are read out by a spectator to the magician on the phone. - Mag...
Wed Aug 19, 2015 2:27 pm UTC
Forum: Language/Linguistics
Topic: ei <-> ie: English speciality?
Replies: 24
Views: 6521

Re: ei <-> ie: English speciality?

Well, English does have words with ei and words with ie where those vowels are pronounced the same, e.g. receive and reprieve. For that vowel sound there is the general rule that after the letter c it's ei and otherwise it's ie, but there are some exceptions. I think that many English people are tau...
Fri Aug 07, 2015 8:43 am UTC
Forum: Science
Topic: A million years
Replies: 59
Views: 8052

Re: A million years

Well, kelvin is a unit of temperature, not intensity. Intensity is the power per area per solid angle . . . per wavelength (W·sr -1 ·m -3 in SI, though you won't usually see it written that way; unfortunately intensity has many definitions in many contexts). In this sense, it is not immediately rel...
Wed Aug 05, 2015 8:06 pm UTC
Forum: Mathematics
Topic: Conjecture about odd prime numbers
Replies: 5
Views: 1667

Re: Conjecture about odd prime numbers

After thinking about it a bit more, you can always take a=(p-1)/2 and b=0.

From Fermat's little theorem, 2^(p-1) == 1 modulo p. Therefore 2^a with a=(p-1)/2 is a number that when squared results in 1 modulo p, so 2^a is 1 or -1.
Wed Aug 05, 2015 3:56 pm UTC
Forum: Mathematics
Topic: Conjecture about odd prime numbers
Replies: 5
Views: 1667

Re: Conjecture about odd prime numbers

Every odd prime number p can be expressed at least once as : p=(2^a + or - 2^b)/k where a and b > 0 a+b < p k some integer > 0 Examples : 5=2^2+2^0 7=2^3-2^0 11=(2^5+2^0)/3 23=(2^11-2^0)/89 Look at the values of +-2^n modulo p. For example with p=11 we have 2^0 == 1, -2^0 == 10 2^1 == 2, -2^1 == 9 ...
Sat Aug 01, 2015 6:52 am UTC
Forum: Mathematics
Replies: 22
Views: 4762

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

It is not really valid to take the (weighted arithmetic) average of two multiplication factors to get the expected multiplication factor. A simpler example would be a 50:50 chance of doubling or halving, which should be neutral in the long run, and not have an average muliplication factor of (2+.5)/...
Thu Jul 30, 2015 8:29 pm UTC
Forum: Mathematics
Topic: New type of pentagonal tile
Replies: 6
Views: 30713

Re: New type of pentagonal tile

My thoughts, in unspecified order: 1. interesting 2. not all text is readable due to the resolution 3. the tiling pattern is pretty complex 4. this isn't published yet, is it? 5. the tile in the picture has a specific combination of values, no independent variable (except for scale obviously). Is i...
Thu Jul 30, 2015 12:50 pm UTC
Forum: Mathematics
Topic: New type of pentagonal tile
Replies: 6
Views: 30713

New type of pentagonal tile

A new type of tileable pentagon has been found! There are many kinds of tiling that use just one shape of pentagonal tile (and its mirror image if necessary). Up to now, these tiles fell into 14 types (see http://www.mathpuzzle.com/tilepent.html ). Now another has been found. type15.png I did a lot ...
Fri Jul 24, 2015 2:45 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 116303

Re: Math: Fleeting Thoughts

I've been reading graph theory -- the definition of adjacency keeps giving me trouble. Everything I read describes adjacency as one of two things: Vertices connected by an edge, or vertices that share an edge. However, both 'connected' and 'shared' confuse me when it comes to directed edges: If X a...
Sat Jul 18, 2015 9:53 pm UTC
Forum: Mathematics
Topic: sum and product of natural number
Replies: 9
Views: 2712

Re: sum and product of natural number

snip If B says yes to the first question, doesn't that mean it could be any number with only two divisors? If B says no then that excludes a=b=1; all a=p, b=1; a=p1, b=p2. Where p, p1, p2 are prime and p1=!p2 The number p1*p2 has four divisors, namely 1, p1, p2, and p1*p2 - there are two ways t...
Fri Jul 17, 2015 8:38 am UTC
Forum: Mathematics
Topic: Pairwise Differences
Replies: 3
Views: 1454

Re: Pairwise Differences

The set of numbers evenly divisible by n is closed under talking the set of pairwise differences. Are there any sets of natural numbers with this property that are not subsets of any set in the above class? In particular, I'm interested in those that, like the above, can be truncated to n elements ...