Search found 2058 matches

by jaap
Fri Nov 06, 2015 1:12 pm UTC
Forum: Logic Puzzles
Topic: Escape the Frictionless Circle
Replies: 156
Views: 38671

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: 1985

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: 1730

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: 5061

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: 5061

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: 1222

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: 3235

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...
by jaap
Thu Oct 08, 2015 5:25 am UTC
Forum: Logic Puzzles
Topic: Timed Bridge Problem
Replies: 5
Views: 3208

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...
by jaap
Mon Oct 05, 2015 1:48 pm UTC
Forum: Mathematics
Topic: Solving diophantine equation
Replies: 5
Views: 1106

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...
by jaap
Fri Oct 02, 2015 10:39 pm UTC
Forum: Logic Puzzles
Topic: Caesar cipher
Replies: 3
Views: 1970

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
by jaap
Fri Oct 02, 2015 12:30 pm UTC
Forum: Logic Puzzles
Topic: How many rooms are there in the tower?
Replies: 26
Views: 4886

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...
by jaap
Wed Sep 30, 2015 9:17 am UTC
Forum: Science
Topic: Speed of waves in water
Replies: 8
Views: 4210

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...
by jaap
Tue Sep 29, 2015 11:26 am UTC
Forum: Science
Topic: Speed of waves in water
Replies: 8
Views: 4210

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.
by jaap
Mon Sep 28, 2015 7:00 am UTC
Forum: Mathematics
Topic: Theoretical problem about traveler salesman
Replies: 6
Views: 1813

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...
by jaap
Wed Sep 23, 2015 5:24 pm UTC
Forum: Mathematics
Topic: geometry [looking at triangles in perspective]
Replies: 7
Views: 1787

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...
by jaap
Wed Sep 23, 2015 2:54 pm UTC
Forum: Mathematics
Topic: geometry [looking at triangles in perspective]
Replies: 7
Views: 1787

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...
by jaap
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: 4571

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...
by jaap
Wed Sep 09, 2015 8:52 am UTC
Forum: Logic Puzzles
Topic: Fill square puzzle
Replies: 4
Views: 1819

Re: Fill square puzzle

The intended answer is of course:
Spoiler:

Code: Select all

....*
.*...
..*..
.*...
.....

XYZ
by jaap
Thu Aug 27, 2015 3:29 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9841
Views: 1642724

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...
by jaap
Fri Aug 21, 2015 6:11 am UTC
Forum: Language/Linguistics
Topic: ei <-> ie: English speciality?
Replies: 24
Views: 5367

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.)
by jaap
Thu Aug 20, 2015 9:16 am UTC
Forum: Logic Puzzles
Topic: Three Cards Trick
Replies: 15
Views: 2478

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...
by jaap
Wed Aug 19, 2015 2:27 pm UTC
Forum: Language/Linguistics
Topic: ei <-> ie: English speciality?
Replies: 24
Views: 5367

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...
by jaap
Fri Aug 07, 2015 8:43 am UTC
Forum: Science
Topic: A million years
Replies: 59
Views: 7530

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...
by jaap
Wed Aug 05, 2015 8:06 pm UTC
Forum: Mathematics
Topic: Conjecture about odd prime numbers
Replies: 5
Views: 1637

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.
by jaap
Wed Aug 05, 2015 3:56 pm UTC
Forum: Mathematics
Topic: Conjecture about odd prime numbers
Replies: 5
Views: 1637

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 ...
by jaap
Sat Aug 01, 2015 6:52 am UTC
Forum: Mathematics
Topic: I don't seem to understand my own brain teaser, please help!
Replies: 22
Views: 4571

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)/...
by jaap
Thu Jul 30, 2015 8:29 pm UTC
Forum: Mathematics
Topic: New type of pentagonal tile
Replies: 6
Views: 30162

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...
by jaap
Thu Jul 30, 2015 12:50 pm UTC
Forum: Mathematics
Topic: New type of pentagonal tile
Replies: 6
Views: 30162

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 ...
by jaap
Fri Jul 24, 2015 2:45 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 107354

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...
by jaap
Sat Jul 18, 2015 9:53 pm UTC
Forum: Mathematics
Topic: sum and product of natural number
Replies: 9
Views: 2550

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...
by jaap
Fri Jul 17, 2015 8:38 am UTC
Forum: Mathematics
Topic: Pairwise Differences
Replies: 3
Views: 1420

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 ...
by jaap
Thu Jul 16, 2015 5:05 am UTC
Forum: Language/Linguistics
Topic: Words You Didn't Know That Describe Things Perfectly
Replies: 91
Views: 24202

Re: Words You Didn't Know That Describe Things Perfectly

Cornobble (archaic): to hit with a fish. Can anyone provide any reference for this being a real thing? The OED online says it isn't, and I can't find any reputable source. I heard it mentioned on the "Says You" podcast, and the host claims to have read it in a book, but I am dubious. I ha...
by jaap
Wed Jul 15, 2015 12:03 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9841
Views: 1642724

Re: Coding: Fleeting Thoughts

I really hate that C++ calls its dynamic array a "vector" - then when I want to use my own type, I have to call it a column_matrix to avoid confusion, even though my type - an immutable, fixed-length, passed by value array that supports scalar addition and xor, scalar multiplication, and ...
by jaap
Tue Jul 14, 2015 10:51 am UTC
Forum: Science
Topic: Conductors and Motors/Generators
Replies: 7
Views: 1687

Re: Conductors and Motors/Generators

Rambling on, it occurred to me that a liquid would be awkward in terms of the brushes, so why not make the winding rigid and allow the magnets to rotate. Then I wondered why all the motors I've seen always rotate the winding - wouldn't it be easier in general to rotate the magnets and avoid the nee...
by jaap
Thu Jul 09, 2015 4:15 pm UTC
Forum: Mathematics
Topic: Marks and Integers
Replies: 3
Views: 1446

Re: Marks and Integers

by jaap
Wed Jul 08, 2015 7:20 am UTC
Forum: Mathematics
Topic: Wanted: Elegant proof of sin(x)/x limit
Replies: 49
Views: 7421

Re: Wanted: Elegant proof of sin(x)/x limit

Qaanol wrote:
jestingrabbit wrote:I claim |BD| < |BE|+|ED|
<snip>
verified by good sense

That’s the part I’m struggling to prove cleanly.

This is the Triangle Inequality and that wiki page has a short euclidean proof.
by jaap
Sun Jul 05, 2015 3:27 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 3912

Re: Factorial expressed as sum of consecutive numbers

Thank you for your comments and computations. Now we assume that the maximal length of the consecutive positive numbers is solved. So we could express n!=S(f,l) where f is the first number of the sequence and l the last number of the sequence. S(f,l) is the summation. The next step is computing S(f...
by jaap
Fri Jul 03, 2015 9:40 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 3912

Re: Factorial expressed as sum of consecutive numbers

Can we conjecture that as n grows the length is ALWAYS an odd number? A factorial can be expressed as equal to A*B where A = 2^k and B an odd number. Limit of the ratio A/B = 0 as n grows to infinity. Does it imply that the length will be always odd? No. You asked for the longest such sequence, whi...
by jaap
Fri Jul 03, 2015 1:05 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 3912

Re: Factorial expressed as sum of consecutive numbers

There is still one hurdle to get over : the complexity. As n grows can we apply this algorithm with minimal complexity. What will be the complexity if n is 500 digits number? I`m not programmer so I just want to know if we can do it in reasonable time. If n is 500 digits, i.e. is about 10^500, then...
by jaap
Fri Jul 03, 2015 12:18 pm UTC
Forum: Mathematics
Topic: Factorial expressed as sum of consecutive numbers
Replies: 25
Views: 3912

Re: Factorial expressed as sum of consecutive numbers

Here's a way to do it. Take 2*n!, and write it as a product a*b, with: - a and b of differing parities (i.e. one is odd and one is even but it does not matter which is which) - a and b as close to each other as possible, (i.e. as near to sqrt(2*n!) as possible) - a<b Then n! is equal to the sum of a...

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