## Search found 55 matches

- Mon Nov 22, 2010 10:23 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 311
- Replies:
**7** - Views:
**3012**

### Re: Problem 311

I think the problem setters were trying to give a hint by choosing N=10000 rather than some other value; I would recommend careful examination of N=10000 and N=5000.

- Sun Nov 21, 2010 9:08 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 311
- Replies:
**7** - Views:
**3012**

### Re: Problem 311

Thank you very much, that was very helpful.

I get the correct answer now (for B(10,000) and B(1,000,000) at any rate), (I'd missed the C0<=B0 inequality, whoops)

I get the correct answer now (for B(10,000) and B(1,000,000) at any rate), (I'd missed the C0<=B0 inequality, whoops)

- Sun Nov 21, 2010 7:28 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 311
- Replies:
**7** - Views:
**3012**

### Problem 311

Are quadrilaterals distinct if: 1) Side lengths are different? 2) Angles are different? 3) Both side lengths and angles are different? (my initial assumption) I've tried computing B(10,000) for each of these but none of them match the answer given (cases 2 and 3 give answers too high, and 1 gives an...

- Wed May 26, 2010 12:20 pm
- Forum: Recreational
- Topic: Nice set theory exercise
- Replies:
**20** - Views:
**7068**

### Re: Nice set theory exercise

Whoops, nice spot Doraki!

Does anyone know of any real world application (e.g. of practical use in engineering or computing) of knowing whether something is uncountable or countably infinite?

Does anyone know of any real world application (e.g. of practical use in engineering or computing) of knowing whether something is uncountable or countably infinite?

- Wed May 26, 2010 7:30 am
- Forum: Recreational
- Topic: Nice set theory exercise
- Replies:
**20** - Views:
**7068**

### Re: Nice set theory exercise

How about:

Elements [floor(x*10**n) for n in [1,2,3,4,...]] where x is a real number such that 0<=x<=1.

e.g. for x=0.1234567 then the element would be {1,12,123,1234,12345,123456,1234567}.

Does this work?

Elements [floor(x*10**n) for n in [1,2,3,4,...]] where x is a real number such that 0<=x<=1.

e.g. for x=0.1234567 then the element would be {1,12,123,1234,12345,123456,1234567}.

Does this work?

- Thu May 13, 2010 9:25 pm
- Forum: News, Suggestions, and FAQ
- Topic: how do I .... generate a "natural number"
- Replies:
**3** - Views:
**1887**

### Re: how do I .... generate a "natural number"

Hi, I'm not sure I have really understood your question, but you may also be interested in investigating numbers such as: 679/500005 = 0.001357986420135... or 13580/100001 = 0.1357986420135.... It is straightforward to generate such numbers by using continued fractions. (Python code) import fraction...

- Sat Mar 20, 2010 1:52 pm
- Forum: Combinatorics
- Topic: Counting solitaire
- Replies:
**2** - Views:
**8692**

### Re: Counting solitaire

Interesting problem to think about, I make the answer 1309302175551177162931045000259922525308763433362019257020678406144 using the Python code (0.03seconds): def derange_cards(J,C): if C==0: return J==0 return sum(nCr(4,k)*nCr(4,j)*nPr(J,j)*nPr(J,k)*derange_cards(J-j+4-k,C-4) for j in range(min(4,J...

- Sun Feb 28, 2010 4:27 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 179
- Replies:
**43** - Views:
**12118**

### Re: Problem 179

26 has factors of 1,2,13,26

25 has factors of 1,5,25

so this pair should not be in your list.

25 has factors of 1,5,25

so this pair should not be in your list.

- Sun Feb 28, 2010 1:21 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 179
- Replies:
**43** - Views:
**12118**

### Re: Problem 179

Does this miss the case n=2 as both 2 and 3 are prime?

- Wed Feb 17, 2010 10:15 am
- Forum: News, Suggestions, and FAQ
- Topic: Categorize Solutions for Different Languages
- Replies:
**1** - Views:
**1171**

### Re: Categorize Solutions for Different Languages

This sounds almost like a Project Euler challenge in itself :) Here's my Python attempt (it's a bit dodgy as it won't always produce correctly formatted html): def forum(problem_id, username, password, lang): params = urllib.urlencode({'username': username, 'password': password, 'login':'Login'}) pa...

- Sun Jan 24, 2010 10:29 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 248
- Replies:
**6** - Views:
**3207**

### Re: Problem 248

I agree with your value for 10. By the way I hope you didn't read the reply too early as I had off by 1 errors in them the first time! I've been really enjoying this site and probably spending far too much time on it. I've been amazed by how much interesting and understandable mathematics I was able...

- Sun Jan 24, 2010 10:08 pm
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 248
- Replies:
**6** - Views:
**3207**

### Re: Problem 248

I make these:

100th is 6239393627

1000th is 6359386477

Good luck!

This probably sounds incredibly patronising, so please understand that no offence is intended, but I suspect you will find it helpful to write a simple bruteforce algorithm to check the results for small numbers

100th is 6239393627

1000th is 6359386477

Good luck!

This probably sounds incredibly patronising, so please understand that no offence is intended, but I suspect you will find it helpful to write a simple bruteforce algorithm to check the results for small numbers

- Sat Jan 09, 2010 8:51 am
- Forum: Recreational
- Topic: Easy and nice
- Replies:
**13** - Views:
**4489**

### Re: Easy and nice

Hmm, have to look into this Y-combinator thing as well

My 2 liner is a bit of a cheat as the first line is quite long, but anyway:

My 2 liner is a bit of a cheat as the first line is quite long, but anyway:

Code: Select all

```
def rec2(x,n): return max([x]+[rec2(10*x+d,n+1) for d in range(10) if (n>1 or d>1) and not (10*x+d)%n])
print rec2(0,1)
```

- Wed Jan 06, 2010 9:32 pm
- Forum: Recreational
- Topic: Easy and nice
- Replies:
**13** - Views:
**4489**

### Re: Easy and nice

That was fun, I get:

36840 for the central 5 digits of the answer (with a Python 2 line program)

36840 for the central 5 digits of the answer (with a Python 2 line program)

- Sun Nov 22, 2009 5:08 pm
- Forum: Combinatorics
- Topic: Gambling
- Replies:
**4** - Views:
**4445**

### Re: Gambling

Pondered this as going to sleep, interesting question :) Spoiler I think a line fits the first regression and a quadratic the second to give the formulae: B/(A+B) and let M=(A-B)/2 -(x-M)^2+(A-M)^2=expected goes when starting from x =>-M^2+A^2-2AM+M^2=A(-2*M+A)=AB when starting from 0. Is this right?