Search found 46 matches

by CCC
Mon Sep 10, 2012 6:08 am UTC
Forum: Mathematics
Topic: Random(probably simple) Combinatorics problem
Replies: 2
Views: 1636

Re: Random(probably simple) Combinatorics problem

A nice little problem. My solution is in the spoiler; it's not obvious, but the final formula is simple enough. Let's look first at the 2x2 case. Consider the first list: "1, 2". Once you've placed these numbers in the final sequence (e.g. x1x2, or 1xx2) there's only on...
by CCC
Mon Aug 27, 2012 6:41 am UTC
Forum: Mathematics
Topic: collection of problems
Replies: 10
Views: 1828

Re: collection of problems

because, if x-(n-1) is divisible by n, then [x-(n-1)]+n = x+1 is divisible by n too. Exactly. You've got your answer, and you've got your proof that it's correct. But I would like to be able to express that more... formally. Be careful. There's a trap here. Laying out a proof formally should mean n...
by CCC
Sun Aug 26, 2012 5:15 pm UTC
Forum: Mathematics
Topic: collection of problems
Replies: 10
Views: 1828

Re: collection of problems

rolo91 wrote:The problem is that I don't know how to proof that this:

(x-1) is divisible by 2
(x-2) is divisible by 3
(....)
(x-9) is divisible by 10


implies this:

(x+1) divides 2,3,4,5,6,7,8,9 and 10


Earlier, you said that:

rolo91 wrote:I know (x+1) divides 2,3,4,5,6,7,8,9. and 10.


How do you know that?
by CCC
Sun Aug 26, 2012 12:47 pm UTC
Forum: Mathematics
Topic: collection of problems
Replies: 10
Views: 1828

Re: collection of problems

What can you say about (x+1)?
by CCC
Tue Aug 21, 2012 6:49 am UTC
Forum: Mathematics
Topic: Problems for Freshpeople
Replies: 9
Views: 2055

Re: Problems for Freshpeople

I'm not sure what a TA is TA - Teaching Assistant. The particulars of the position will vary from place to place; at the university I was at, the TA would be expected to mark certain assignments (ones that didn't count much towards the final mark), occasionally go through homework problems with the...
by CCC
Tue Aug 14, 2012 12:36 pm UTC
Forum: Mathematics
Topic: Weighting time spans by age, etc.
Replies: 6
Views: 1482

Re: Weighting time spans by age, etc.

Let me compare six months (0.5 years), starting from the 13th or 25th birthday, as a worked example: 0.5 years starting at the 13th birthday: y=13, z=0.5. Length of subjective time experienced: ln(13.5)-ln(13)=0.03774 0.5 years starting at the 25th birthday: y=25, z=0.5. Length of subjective time e...
by CCC
Tue Aug 14, 2012 11:48 am UTC
Forum: Mathematics
Topic: Weighting time spans by age, etc.
Replies: 6
Views: 1482

Re: Weighting time spans by age, etc.

That's pretty straight forward, but I think it's the other way around to what I was having in mind. Two hours at age thirteen don't feel like just over one twenty-five-year-old hour; the younger hours feel longer. If you multiply by b/a, you get three hours and fifty minutes of 25-year-old time out...
by CCC
Tue Aug 14, 2012 10:09 am UTC
Forum: Mathematics
Topic: Weighting time spans by age, etc.
Replies: 6
Views: 1482

Re: Weighting time spans by age, etc.

Let me take the experience of one second at age 1 as a baseline; call that an experienced time of 1 second. At age 2, that second appears half as long in comparison to my age, so that's an experienced time of 0.5. At age four, similarly, that's an experienced time of 0.25. At age x, that's an experi...
by CCC
Tue Aug 14, 2012 7:43 am UTC
Forum: Mathematics
Topic: Collatz conjecture
Replies: 11
Views: 2961

Re: Collatz conjecture

Choosing a multiple of three would be a good idea. Hmmm. A multiple of three cannot be part of a loop; 3x+1 can never lead to a multiple of 3, and x/2 can only lead to a multiple of 3 if starting from a multiple of three. Thus, no multiple of 3 can be reached from any smaller number at any point, n...
by CCC
Mon Aug 13, 2012 8:44 am UTC
Forum: Mathematics
Topic: Collatz conjecture
Replies: 11
Views: 2961

Re: Collatz conjecture

I've been thinking about this conjecture... and I think I may be partway to a proof, though under completely different lines to the original poster. First of all, I'll take a slightly modified version of the conjecture. If x is even, I divide by two; if x is odd, I multiply by three and add one. (Th...
by CCC
Fri Aug 03, 2012 7:39 am UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 28117

Re: The Shortest String Containing all Permutations of n Sym

It's obvious that any two permutations which share the same n+1 digit will 'contract' to two distinct permutations like I want them to. I had been assuming that all the interesting cases were of this sort. However, I also think CCC is right, that the issue is when you have two permutations that sha...
by CCC
Thu Aug 02, 2012 2:55 pm UTC
Forum: Mathematics
Topic: The Shortest String Containing all Permutations of n Symbols
Replies: 29
Views: 28117

Re: The Shortest String Containing all Permutations of n Sym

If you remove all of the digits 'n+1', the string will then (as above) contain at least n+1 copies of each of the n! permutations of the digits 1,...,n. I think that's not quite right. Consider the sequence of digits 41234. This contains two unique length-four sequences (4123 and 1234), but removin...
by CCC
Mon Jul 30, 2012 7:52 am UTC
Forum: Mathematics
Topic: A Thread for scratch123's Random Math Questions
Replies: 71
Views: 16114

Re: Sum of digits and base n

I don't think Benford's Law applies here; it's applicable to random distributions with positive skew and a mean greater than the median. It's not applicable to a uniformly distributed random number, and the distribution of all integers should match that of a uniformly distributed random integer, sur...
by CCC
Sat Jul 28, 2012 7:05 pm UTC
Forum: Mathematics
Topic: A Thread for scratch123's Random Math Questions
Replies: 71
Views: 16114

Re: Sum of digits and base n

If, and only if, the sum of the digits of a positive integer n in base B adds up to a multiple of (B-1), then n is itself a multiple of (B-1). This can be applied recursively; you can find the sum of the digits of n, and then the sum of the digits of that, and so on, continuing until the result if o...
by CCC
Mon Jul 23, 2012 1:12 pm UTC
Forum: Mathematics
Topic: Largest 3 consecutive semi-primes?
Replies: 19
Views: 6029

Re: Largest 3 consecutive semi-primes?

So, are you sure those are the lowest 7-chains? If smaller 7-chains exist, then there is a bug in my program. It's not impossible. To put that lowest sequence in terms of prime factors: (7*11*2749; 2*3*35279; 5*5*8467; 2*2*52919; 3*37*1907; 2*109*971; 13*19*857) Also, can there be two 7-chains that...
by CCC
Mon Jul 23, 2012 9:06 am UTC
Forum: Mathematics
Topic: Largest 3 consecutive semi-primes?
Replies: 19
Views: 6029

Re: Largest 3 consecutive semi-primes?

7-chains exist. I threw together a piece of C code and did a quick brute-force search. The lowest sequence found was (211673; 211674; 211675; 211676; 211677; 211678; 211679) - the highest prime factor in that sequence was 52919. Sequences: (211673; 211674; 211675; 211676; 211677; 211678; 211679&...
by CCC
Sun Jul 22, 2012 10:29 am UTC
Forum: Mathematics
Topic: Largest 3 consecutive semi-primes?
Replies: 19
Views: 6029

Re: Largest 3 consecutive semi-primes?

Okay, so you've got six primes, p, q, r, s, t and u, where p*q+1=r*s and r*s+1=t*u. The lowest triple is <33, 34, 35>. Since 4 cannot be part of such a triple, no triple may include a multiple of 4. Therefore, p*q-1 and t*u+1 must both be multiples of 4. Therefore, r*s is even. Therefore, either r o...
by CCC
Tue Jul 17, 2012 7:09 am UTC
Forum: Mathematics
Topic: Proof preference
Replies: 6
Views: 2127

Re: Proof preference

I think I prefer it when the lemmas are presented first, one after the other. Then I can run from the top of the proof to the bottom, checking that every step follows from the previous step, until I get to the end; I don't have to go back and forth, nor do I have to remember which lemmas remain unpr...
by CCC
Sat Jul 14, 2012 7:37 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

All linear transformations on R 2 (the vector space of pairs of real numbers) are completely defined by where they take (1,0) and (0,1). It isn't hard to build the matrix once you know where they go -- the first column of the matrix is where it takes (1,0) and the second column where it takes (0,1)...
by CCC
Thu Jul 12, 2012 8:04 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Just started learning about matrices. Question; what is the practical application of matrices? Why the seemlingly arbitrary multiplication rules? I want to understand the point behind what I'm doing rather than just learn to go through the motions. Let me demonstrate merely a single practical appli...
by CCC
Thu Jul 12, 2012 7:36 am UTC
Forum: Mathematics
Topic: How can I tell if Im good at "Real Math"? + Emphasis anxiety
Replies: 11
Views: 4785

Re: How can I tell if Im good at "Real Math"? + Emphasis anx

I think I'm decent at math, but I feel like about 90% of that is me faking it. There's a simple test that will tell you if you are, in fact, faking it or not. Are you getting the right answers, consistently? If yes, then you are not faking it. If no, then I'd argue that you are not 'decent at math'...
by CCC
Mon Jul 09, 2012 2:31 pm UTC
Forum: Mathematics
Topic: Seating around a Table
Replies: 12
Views: 3851

Re: Seating around a Table

In how many ways, order matters, can 14 married couples be seated in chairs consecutively 1 to 28 at a round table so that one man is always between two women and no man ever sits next to his wife? Do you mean so that each man is between two wonen, thus mwmwmwmw... or so that at least one man is be...
by CCC
Sun Jul 08, 2012 7:15 pm UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

New math question, is there a trick to factoring polynomials with prime numbers? In most cases I can get the answer just by looking at it, the general pattern seems to be something like (1st nx + or - 1)(x + or - last n), as in 3x^2 - 29x - 10 = (3x + 1)(x - 10). But of course they don't all do tha...
by CCC
Thu Jul 05, 2012 9:57 pm UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Ccc, I've put your link in my reading list, thanks for the lesson. I'm really curious as to how light is measured at the same speed no matter what speed you're moving at. Hawking says it's because everyone experiences time differently, I'm still trying to work out that concept. His special on time ...
by CCC
Thu Jul 05, 2012 7:41 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Linear simultaneous equations? You mean this? Because that seems pretty simple. In fact I'm glad you led me to look that up, I just learned something new. :P Yes, that's exactly what I mean. Now, I'm only going to go into Special Relativity; General Relativity is a whole different story (and uses s...
by CCC
Wed Jul 04, 2012 6:23 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Thanks for the insight, there's so much I don't know that I want to understand. I thought math was the only real obstacle (I only ever considered math to be my dyslexia, everything else was learnable in theory) but it looks like I'll have to tackle a lot of difficult concepts in a broad spectrum. W...
by CCC
Mon Jul 02, 2012 8:19 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Also: - 81(x^8)(y^6) / 39 (x^9)(y^4) = -27(y^2) /13x That looks like simplifying fractions, both numbers can be divided by 3 to get that result, did the others stay the same because they can't be simplified anymore? Is there a trick to this I'm not seeing? You have the problem exactly; it is simpli...
by CCC
Sun Jul 01, 2012 11:09 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

On the subject of negative and positive numbers and multiplication; this goes back to the definition of multiplication at repeated addition. a*b is simply (a+a+...+a) with b a's. So: 2*3=2+2+2 3*7=3+3+3+3+3+3+3 4*5=4+4+4+4+4 This leads immediately to a consequence; (a*b)+(a*c) = (a+a+...{b times}......
by CCC
Sat Jun 30, 2012 5:03 pm UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

I would like to add that you should really try and take a lot away from your first question and dopefish's response. I agree wholeheartedly with Birk. Dopefish's answers to your first and third question did not give rise to long discussions, because they do not lend themselves to extended discussio...
by CCC
Fri Jun 29, 2012 8:12 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Also... Given the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 I thought the answer stops at -16x - 7, but the detailed solution continues. Add 16x + 7 to both sides and write the equation as follows 0 = 0 Why do that? @.@ Why not? It's a valid step, and you can take any valid step you like at a...
by CCC
Fri Jun 29, 2012 6:42 am UTC
Forum: Mathematics
Topic: Linear-time arithmetic prime test yields factors
Replies: 13
Views: 4515

Re: Linear-time arithmetic prime test yields factors

BlueNight wrote:What I'd need for a real test is an optimized big-int library.


You might find libgmp useful, then. Just watch the initialisation and clearing of the variables.
by CCC
Wed Jun 27, 2012 9:41 am UTC
Forum: Mathematics
Topic: The Most Important Math
Replies: 48
Views: 19397

Re: The Most Important Math

I think that The Secret Number is relevant at this point. -------------- What is the most important branch of mathematics? That depends. Important is defined as "Having relevant and crucial value". In order for it to be most important, therefore, it has to be both highly relevant and highl...
by CCC
Mon Jun 25, 2012 7:55 am UTC
Forum: Mathematics
Topic: Want to study astronomy... bad at math
Replies: 117
Views: 30813

Re: Want to study astronomy... bad at math

Math is a skill. It can be learnt, and yes, it can be learnt at any age. What you need for best results are a good teacher, a clear willingness to learn, and a lot of practice. With a bit of effort, a lot of luck, and the right study materials, it may be possible to manage without the good teacher, ...
by CCC
Sat Jun 23, 2012 9:23 pm UTC
Forum: Mathematics
Topic: Polynomials with integer coefficients
Replies: 1
Views: 841

Polynomials with integer coefficients

For a polynomial a 1 x n +a 2 x n-1 +a 3 x n-2 +---+a n-1 x+a n =0, where the coefficients a 1 , a 2 , a 3 , --- a n-1 ,a n are all integers and a 1 is nonzero, all rational solutions for x will have denominators that are factors of a 1 when written in the simplest form. This holds for all polynomia...
by CCC
Fri Jun 22, 2012 4:01 pm UTC
Forum: Mathematics
Topic: Making the most out of a djinn's offer
Replies: 14
Views: 3243

Re: Making the most out of a djinn's offer

Ask for one dollar for every digit in the decimal expansion of pi. Of course, that's assuming you want an infinite amount of money and won't be crushed by the weight of the dollar bills... also, you don't then have a 50% chance of ending up with only $4. But yes, infinity is very strange. Consider t...
by CCC
Thu Jun 21, 2012 8:36 am UTC
Forum: Mathematics
Topic: The graph of one to the power x
Replies: 10
Views: 3159

Re: The graph of one to the power x

If and only if there is some rational number r such that pi+r*e is rational, then they will share a root. Since, as is indicated above, the question remain unresolved even for the case of r=1, we may indeed have some trouble. On the bright side, I can say with certainty that when r=0, pi+r*e is irra...
by CCC
Thu Jun 21, 2012 8:30 am UTC
Forum: Mathematics
Topic: Stuck on an easy-looking combinatorial problem
Replies: 3
Views: 1018

Re: Stuck on an easy-looking combinatorial problem

This problem is indeed solvable by induction. Consider the two-element case: {a, b} The only difference here is a-b, which has multiplicity of 1. This is less that or equal to 1 2 . Therefore, your formula is valid at n=2. Now, assume the formula valid for n, and see if this allows proof that it is ...
by CCC
Thu Jun 21, 2012 8:12 am UTC
Forum: Mathematics
Topic: Simple yet varied functions that generate the same number
Replies: 5
Views: 1527

Re: Simple yet varied functions that generate the same numbe

Let us say that we limit ourselves to plus, minus, times, divide, exponentiation, and roots. That's six possible operators. Including parenthesis merely means that we can arbitrarily apply these operators in any order, so let us include parenthesis. Numbers; let us limit ourselves to using exactly t...
by CCC
Wed Jun 20, 2012 8:09 am UTC
Forum: Mathematics
Topic: The graph of one to the power x
Replies: 10
Views: 3159

Re: The graph of one to the power x

With the condition that kj-1 cannot be 0, since otherwise dividing by it is a bad idea. This would imply that both k and j are 1 (or both are -1, but that's basically the same), so the first two equations would be, substituting this in: a + c = b b + d = a So, a + c can (and trivially does) share a...
by CCC
Tue Jun 19, 2012 7:46 am UTC
Forum: Mathematics
Topic: The graph of one to the power x
Replies: 10
Views: 3159

Re: The graph of one to the power x

What I don't know is whether all irrational numbers have the same set of roots or not. Or even how to tell whether two given irrational numbers have the same set of roots. Would 1 pi and 1 e share any roots besides 1? No they do not, and no they do not. That's what I would expect, but can you prove...

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