Search found 53 matches

by uws8505
Mon Dec 08, 2008 11:07 am
Forum: Combinatorics
Topic: monocoloured triangle
Replies: 5
Views: 3075

Re: monocoloured triangle

For 1), let's think of a special case k=3. To get at least three points of the same color, we need equally spaced 7 points on the circle. However, that does not guarantee of an isosceles triangle. Then we go to the next step. Equally spaced 10 points on the circle give at least 4 points of the same ...
by uws8505
Mon Dec 08, 2008 10:43 am
Forum: Number
Topic: Primes of the Fibonacci Sequence
Replies: 11
Views: 4357

Re: Primes of the Fibonacci Sequence

stijn263 wrote:Also pretty amazing is gcd( Fm , Fn ) for any n,m > 1
I think you missed gcd(Fm,Fn) =something, maybe gcd(m,n)?
by uws8505
Mon Dec 08, 2008 10:36 am
Forum: Combinatorics
Topic: monocoloured triangle
Replies: 5
Views: 3075

Re: monocoloured triangle

I think it's a very simple problem. Think of a set of five points on a regular pentagon inscribed in the circle. Then all triangles that can be made of three points in the set are isosceles triangles.(1) Now apply pigeonhole principle. Then there are three points of the same color.(2) Combining (1) ...
by uws8505
Sat Dec 06, 2008 6:40 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 072
Replies: 36
Views: 9577

Re: Problem 72

n <= 100 case is too small.
by uws8505
Fri Dec 05, 2008 1:55 am
Forum: Combinatorics
Topic: points of 2 colours in the plane
Replies: 9
Views: 3760

Re: points of 2 colours in the plane

jaap wrote:Can you show that by repeatedly uncrossing pairs that you eventually arrive at a situation with no intersections?
I thought about it when I posted (partial) solution, but I can't find way to prove it yet :(
by uws8505
Thu Dec 04, 2008 10:54 am
Forum: Combinatorics
Topic: points of 2 colours in the plane
Replies: 9
Views: 3760

Re: points of 2 colours in the plane

I haven't seen this problem before, but I get the key idea of it. First, randomly draw the segments so that each of the red points is connected to one blue point. If there is no intersection, the problem is over. If two of the segments intersect, then erase them and draw two segments in the other wa...
by uws8505
Wed Dec 03, 2008 4:58 am
Forum: News, Suggestions, and FAQ
Topic: Alt text on math symbols
Replies: 18
Views: 5850

Re: Alt text on math symbols

stijn263 wrote:I was wondering, what is the value of 3^3^3 ? Is it 3^27 or 27^3? Maple returns:
Error, ambiguous use of `^`, please use parentheses
Mathematica gives 3^3^3 = 3^27 = 7625597484987, not 27^3 = 19683. Maybe the order of ^ operation is right-to-left.
by uws8505
Fri Nov 28, 2008 12:44 am
Forum: Discrete Mathematics
Topic: A Cicle Pattern
Replies: 7
Views: 3487

Re: A Cicle Pattern

elendiastarman wrote:Draw line segments from the non-base sides of the triangle (I'll just call these "sides" from now on) to the center of the circle.
Should I draw line segments from midpoints of the sides to the center of inscribed circle?

Also, where is the blue portion that you mentioned in the original problem?
by uws8505
Tue Nov 25, 2008 1:37 pm
Forum: News, Suggestions, and FAQ
Topic: Code optimization techniques
Replies: 20
Views: 5849

Re: Code optimization techniques

Oh, thanks for your help.
by uws8505
Tue Nov 25, 2008 9:57 am
Forum: Discrete Mathematics
Topic: A Cicle Pattern
Replies: 7
Views: 3487

Re: A Cicle Pattern

Then why there is a blank box on this page and "link unavailable" error message when clicking the link when I try to see the picture?
Because I am using the Internet in South Korea? :(
by uws8505
Tue Nov 25, 2008 9:52 am
Forum: News, Suggestions, and FAQ
Topic: Code optimization techniques
Replies: 20
Views: 5849

Code optimization techniques

May I have some of the techniques used frequently to optimize a program i.e. to decrease time taken to get an answer?

For example, building a list is often better than branched recursion(at least I think this one is correct, but I'm not sure)
by uws8505
Mon Nov 24, 2008 12:59 pm
Forum: Discrete Mathematics
Topic: A Cicle Pattern
Replies: 7
Views: 3487

Re: A Cicle Pattern

Sorry, but your picture is invisible...
by uws8505
Mon Nov 10, 2008 8:13 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 147
Replies: 9
Views: 4273

Re: Problem 147

I'm trying to solve it but I haven't found any algorithm to find the number of cross hatched ones yet :(
by uws8505
Mon Nov 10, 2008 7:59 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 147
Replies: 9
Views: 4273

Re: Problem 147

I get 420 for a 5*7 grid, but I'm not so sure about my answer.
by uws8505
Mon Nov 10, 2008 7:19 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 009
Replies: 47
Views: 14099

Re: What format to enter an answer?

As indicated in the problem, you should enter the product of the three numbers a*b*c.
by uws8505
Sun Nov 09, 2008 10:59 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 018
Replies: 50
Views: 14738

Re: Problem #18

btilly wrote:A greedy algorithm will not find it.
But I used some variation of greedy algorithm to get to the solution and solved it.
by uws8505
Wed Nov 05, 2008 10:25 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 060
Replies: 40
Views: 15617

Re: Problem #60

The primes shown may or may not be included in the new set of 5 primes.

1 is NOT a prime number.
by uws8505
Mon Nov 03, 2008 8:59 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 139
Replies: 5
Views: 2029

Re: Problem 139

There are much more triangles whose side lengths are relatively prime, at least I think.
by uws8505
Sun Oct 19, 2008 3:22 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 138
Replies: 22
Views: 6326

Re: problem 138

Then write another function that gives floor of sqrt of an integer, and test whether its square matches original value.
by uws8505
Wed Oct 15, 2008 11:24 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 004
Replies: 83
Views: 16711

Re: Problem 4 - palindroms

It would be better if you test (999,999) (999,998) (999,997) (998,998) (999,996) (998,997) and so on
rather than (999,999),...,(999,100),(998,999),...