Search found 352 matches

by thundre
Sat Apr 23, 2016 11:28 pm
Forum: Applied Mathematics
Topic: Monte Carlo pdf
Replies: 0
Views: 1473

Monte Carlo pdf

I'm looking for a statistical technique to determine whether two sampled pdfs are the same. I know I'm not going to get an absolute answer, but I'd like to get some kind of measure of confidence. This is for a software regression test. The software runs a Monte-Carlo simulation, meaning that there's...
by thundre
Wed Aug 27, 2014 12:55 pm
Forum: Recreational
Topic: Numbers built of short primes
Replies: 1
Views: 949

Re: Numbers built of short primes

This problem really doesn't have much to do with primality. Primes are just an easy way to specify a permitted set of substrings of a given length. The use of base 10 means only {1,3,7,9} can appear any place other than the first 4 digits. IMHO it would be a more interesting problem in a prime base ...
by thundre
Fri Aug 15, 2014 1:33 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 012
Replies: 99
Views: 19835

Re: Problem 012

If you have two while loops nested, the outer condition is only checked when the inner loop exits. In your case, your inner condition will never be false, so the inner loop becomes infinite.

I also question whether you even need two nested loops for your purpose. I think one would be enough.
by thundre
Sun Aug 10, 2014 7:11 am
Forum: Discrete Mathematics
Topic: Network Effect
Replies: 5
Views: 1812

Re: Network Effect

More results, from an exact algorithm (which also uses Java and BigInteger). E(100) = 81.4240329218325 E(200) = 159.63192084627659 E(300) = 237.27431487414844 E(400) = 314.62439473407545 E(500) = 391.7877747430619 E(600) = 468.8185771837519 E(700) = 545.7489380680325 E(800) = 622.5997897966862 E(900...
by thundre
Thu Aug 07, 2014 5:41 pm
Forum: Number Theory
Topic: Analytical simple proof of Fermat's last theorem ????
Replies: 20
Views: 4904

Re: Analytical simple proof of Fermat's last theorem ????

I have not finished reading, but you have an error in your theorem. 1 1 +3 1 =4 1 Obviously 1 and 3 are both odd which means your main theorem is incorrect. Likely there is some reason for n>1. If there is no obvious reason for this, then there is a fault deeper in your proof well n=1 is a trivial ...
by thundre
Wed Aug 06, 2014 9:18 pm
Forum: Discrete Mathematics
Topic: Network Effect
Replies: 5
Views: 1812

Re: Network Effect

I get 81.4243077, but to save time and memory, my algorithm only considers 0.9999942 of all cases.
by thundre
Mon Aug 04, 2014 4:51 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 004
Replies: 83
Views: 10179

Re: Problem 004

nanogyth wrote:
thundre wrote:If you assume the first digit of the answer is 9, the last digit must also be 9. Then you can infer it's either xx1 * xx9 or xx3 * xx3.
or xx7 * xx7
Of course.

Image(Doh!)
by thundre
Mon Aug 04, 2014 2:32 pm
Forum: News, Suggestions, and FAQ
Topic: How to access the PDF containing answer explanations ?
Replies: 2
Views: 4345

Re: How to access the PDF containing answer explanations ?

rayfil wrote:... is being rewritten to make it more secure and hopefully will become available within the next few weeks along with the PDFs.
Rayfil, that is great news!

Perhaps the fact that the team has shifted from damage assessment to rebuilding should be mentioned at http://projecteuler.net/news?
by thundre
Fri Aug 01, 2014 6:51 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 004
Replies: 83
Views: 10179

Re: Problem 004

Is there are a more efficient solution to this problem than O(n^2)? I think all general algorithms will take O(n 2 ), but the clever ones have a much lower constant. You could go crazy optimizing. For example, 10 is an even base. If you assume the first digit of the answer is 9, the last digit must...
by thundre
Tue Jul 22, 2014 12:07 pm
Forum: News, Suggestions, and FAQ
Topic: Web site off line Jun 15, 2014
Replies: 55
Views: 16576

Re: Web site off line Jun 15, 2014

I personally have no intention of jumping ship on PE and don't mind waiting for however long it may take. Just don't consider jumping ship on PE yourself. :D PE is so much geeky fun for so many of us. I want to second oleglyamin 's words of encouragement. PE is a lot of fun, and the locked solution...
by thundre
Fri Jul 18, 2014 4:53 pm
Forum: Number
Topic: Brut Force?
Replies: 8
Views: 2957

Re: Brut Force?

There are following integers 1,3,4,6 and you have to use the ordinary mathematic calculation rules like (+; -; /; *) addition, subtraction, division and multiplication. The result must be 24. 6*(1+4)-3 = 21 (so this is just an example). I think you can hit all cases by varying the following: Which ...
by thundre
Thu Jul 17, 2014 4:51 pm
Forum: Discrete Mathematics
Topic: Ex-Increasing Set Sequence
Replies: 7
Views: 1902

Re: Ex-Increasing Set Sequence

Excellent work, thundre . I've been busy for some time recently and couldn't work on this problem. The conjecture quantheory suggested seems to be false from the sample sequences (seeing {2,8} instead of {5} in L(10) and many others), and also my own thought of symmetry (formally: {x 1 ,...,x i } i...
by thundre
Tue Jul 15, 2014 4:09 pm
Forum: Discrete Mathematics
Topic: Ex-Increasing Set Sequence
Replies: 7
Views: 1902

Re: Ex-Increasing Set Sequence

Here are some more results, with example sequences and the maximum size set in each example. L(1) = 1: peak size 1 -- {1} L(2) = 2: peak size 1 -- {1} {2} L(3) = 3: peak size 1 -- {1} {2} {3} L(4) = 5: peak size 2 -- {1} {2} {1,4} {3} {4} L(5) = 7: peak size 2 -- {1} {2} {1,4} {3} {2,5} {4} {5} L(6)...
by thundre
Thu Jul 10, 2014 10:13 pm
Forum: Discrete Mathematics
Topic: Ex-Increasing Set Sequence
Replies: 7
Views: 1902

Re: Ex-Increasing Set Sequence

The obvious node-based algorithm uses O(2 n ) memory and O(4 n ) time at most. It runs very fast up to n=18. Process each subset in order of average. Discard supersets with the same average. Keep a list of subsets sorted by maximum position. For each subset you process, look back in the list to find...
by thundre
Wed Jul 02, 2014 9:04 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 371
Replies: 33
Views: 11878

Re: Problem 371

The inputs are independent. The probability of seeing a given number at a given time is 1/1000.

What I was saying was that the probability of a win at (for example) the 6th license plate depends on the values of the first 5 plates -- in particular, whether any were duplicated.
by thundre
Wed Jul 02, 2014 8:50 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 300
Replies: 9
Views: 3306

Re: Problem 300

oleglyamin wrote:Could anyone tell me how fast the program is expected to be? I'm a little over 1 minute here. Is it one of those problems where you can't write a program much much faster than 1 min? Thanks.
Mine finds the correct answer in 1.5 sec, and it runs in Java. I suspect C++ could do the job in 200-400 ms.
by thundre
Wed Jul 02, 2014 8:00 pm
Forum: Number
Topic: Square root of -1 in Fp
Replies: 1
Views: 1911

Re: Square root of -1 in Fp

Considering that each base has 2 roots of -1, and that this pattern only holds for 3 low cycles, I'd say yes it's as much of a coincidence as any deterministic bit of math.

http://en.wikipedia.org/wiki/Strong_Law ... ll_Numbers
by thundre
Mon May 26, 2014 5:26 pm
Forum: Combinatorics
Topic: Set containing max number of subsets
Replies: 11
Views: 3463

Re: Set containing max number of subsets

This could be done with dynamic programming, for some cases. The state would be the set built so far and the score so far (number of target subsets included). Start with the empty set, which has a score of 0. Iterate over the list of target subsets. For each state, calculate the union of the set and...
by thundre
Tue May 13, 2014 6:06 pm
Forum: News, Suggestions, and FAQ
Topic: [Suggestion]A Way to Avoid Answer Copy
Replies: 2
Views: 1290

Re: [Suggestion]A Way to Avoid Answer Copy

I think it is quite easy to achieve, for each problem, assign a different question for each user according to user ID or randomly. Eg., for user 1, ask how many xxx in 1e10, while for user 2, ask how many xxx in 1.2e10. This means every user need to solve the problem independently or at least got t...
by thundre
Tue May 13, 2014 12:10 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 205
Replies: 27
Views: 9804

Re: Problem 205

Is there someone I can discuss (PM) this with, because I feel like it is possible to solve it this way, but I'm making a mistake somewhere... And it would help to write it down, and probably someone does know how to do it this way. You can PM me if you wish. But I think I can explain what's wrong w...