Search found 515 matches

by jaap
Wed Oct 17, 2018 8:46 am
Forum: Number
Topic: "Fixed Points"
Replies: 5
Views: 132

Re: "Fixed Points"

Oh, it's the unmistakable work of Raymond Smullyan. The strings we are working with are expressions. Just like an ordinary arithmetical expression like "4+5" can be evaluated to yield "9", these strings have their own type of arithmetic that can be used to evaluate them and yield another string. You...
by jaap
Tue Oct 16, 2018 6:30 am
Forum: Number
Topic: "Fixed Points"
Replies: 5
Views: 132

Re: "Fixed Points"

kenbrooker wrote:
Mon Oct 15, 2018 9:47 pm
In this case, X is a string and X is a function, a function of itself.
In what case? In what context do you have strings that are also functions?

It is hard to tell what misunderstandings you might have if you don't show the original text that you might be misunderstanding.
by jaap
Tue Oct 02, 2018 12:36 pm
Forum: Resources
Topic: Please Help re UVa @ https://uva.onlinejudge.org
Replies: 7
Views: 121

Re: Please Help re UVa @ https://uva.onlinejudge.org

Main.java:2: error: class aUVa100 is public, should be declared in a file named aUVa100.java It IS "declared in a file named aUVa100.java" but... I don't know the online IDE/compiler this site uses, and I don't think I can access it without becoming a member. It clearly thinks it is in a file calle...
by jaap
Mon Oct 01, 2018 7:57 am
Forum: Resources
Topic: Please Help re UVa @ https://uva.onlinejudge.org
Replies: 7
Views: 121

Re: Please Help re UVa @ https://uva.onlinejudge.org

Maybe you need to make the class public for it to run:

Code: Select all

public class aUVa100
by jaap
Tue Sep 25, 2018 6:14 pm
Forum: News, Suggestions, and FAQ
Topic: Progress Page turned orange.
Replies: 1
Views: 49

Re: Progress Page turned orange.

See euler's post here:
viewtopic.php?f=5&t=6663#p52409
by jaap
Fri Sep 07, 2018 12:03 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 012
Replies: 99
Views: 19835

Re: Problem 012

sriramrajan wrote:
Fri Sep 07, 2018 9:04 am
My answer has 112 divisors / factors and is the first one in the series but was declared wrong.
The question is not asking for the first one with 112 divisors, but for
... the first triangle number to have over five hundred divisors?
by jaap
Sat Jul 28, 2018 11:42 am
Forum: News, Suggestions, and FAQ
Topic: Mark problems that can be figured out through math alone
Replies: 3
Views: 168

Re: Mark problems that can be figured out through math alone

There is a thread on this forum discussing which problems can be solved with paper and pencil:
viewtopic.php?f=12&t=1982
by jaap
Thu Jul 19, 2018 9:53 am
Forum: News, Suggestions, and FAQ
Topic: Add problem categories
Replies: 1
Views: 93

Re: Add problem categories

This has been asked before. Here is a previous answer:
viewtopic.php?f=5&t=3837&p=41793#p41793
by jaap
Tue Jul 10, 2018 1:49 pm
Forum: Number
Topic: an old maths olympiad question
Replies: 27
Views: 799

Re: an old maths olympiad question

... hence $\sin 4x=\sin 3x$ implies $\sin(\pi-4x)=\sin 3x$ Nicely done. This is the trick that I missed. I thought we would have to go all the way up to $\sin(7x)$, which would be horrible. NOTE: All this in hindsight knowing that n should be 7. To derive it in an Olympiad is close to impossible fo...
by jaap
Mon Jul 09, 2018 3:21 pm
Forum: Number
Topic: an old maths olympiad question
Replies: 27
Views: 799

Re: an old maths olympiad question

So people here can't solve an Olympiad question I probably could but I can't be bothered. Spending a couple of minutes here and there during breaks at work is rather different from actually solving it in Olympiad. Olympiad questions are often hard until some specific insight hits you, and it can ta...
by jaap
Mon Jul 09, 2018 12:28 pm
Forum: Number
Topic: an old maths olympiad question
Replies: 27
Views: 799

Re: an old maths olympiad question

I can derive a cubic equation that cos(x) must satisfy where x is half the central angle, i.e. x=180/n. It is straightforward to see that: A1A2 = 2sin(x) A1A3 = 2sin(2x) A1A4 = 2sin(3x) Substituting this in the equation, and using the angle sum formulae sin(a+b)=sin(a)cos(b)+sin(b)cos(a) and cos(2a)...
by jaap
Mon Jul 09, 2018 9:02 am
Forum: Number
Topic: an old maths olympiad question
Replies: 27
Views: 799

Re: an old maths olympiad question

Far as I know, a "regular" polygon has sides of equal length, call it length S, so: 1/A1A2 = 1/A1A3 + 1/A1A4 is the same as 1/S^2 = 1/S^2 + 1/S^2, the same as 1 = 1 + 1 so No polygon satisfies... I could be missing something but did you say there were 10 questions? A 1 , A 2 , A 3 , A 4 are consecu...
by jaap
Sun Jul 08, 2018 6:27 am
Forum: Number
Topic: an old maths olympiad question
Replies: 27
Views: 799

Re: an old maths olympiad question

Whatever the missing question is, its answer probably relies on the fact that that polynomial can be written as (n-2)(n-1)n(n+1)(n+2)(n+3)+3. I have updated ot now. Is it my inexperience that I cannot see how to factor the polynomial? No. I cheated and typed it into Wolfram Alpha. If I were in a co...
by jaap
Sat Jul 07, 2018 2:58 pm
Forum: Number
Topic: an old maths olympiad question
Replies: 27
Views: 799

Re: an old maths olympiad question

S_r wrote:
Sat Jul 07, 2018 3:38 am
The question:
Prove that for no integer n, n6+3n5-5n4-15n3+4n2+12n+3
Whatever the missing question is, its answer probably relies on the fact that that polynomial can be written as
(n-2)(n-1)n(n+1)(n+2)(n+3)+3.
by jaap
Wed Jul 04, 2018 6:59 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 141
Replies: 27
Views: 8169

Re: Problem 141

I keep getting the same numbers as Erf_Erf, I've tried a few different approaches and keep getting 23261047907 for 10^10. Can I show my numbers to someone to see what I'm missing? That number is too high. The difference to what it should be is a 10-digit square so probably you have one errant entry...
by jaap
Thu May 17, 2018 9:14 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 080
Replies: 33
Views: 6441

Re: Problem 80

There is already a thread for problem 080 here.
In it you will find the answer to your question, which is that the first digit in your example is actually 5.
by jaap
Fri Feb 23, 2018 10:32 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 085
Replies: 9
Views: 1742

Re: Problem 085

Your answer is a near miss - it is a just little over 2000000 - but you can get closer.
Remember that you can also get close to 2000000 by being just under it.
by jaap
Fri Jan 12, 2018 3:51 pm
Forum: Recreational
Topic: Winning Lottery with Prime Number!?
Replies: 7
Views: 1043

Re: Winning Lottery with Prime Number!?

There are 15 primes in the range [1,49]. There are 15C7 + 34C1*15C6 = 176605 ways to choose at least 6 of those primes in a drawing of 7 balls. There are 49C7 = 85900584 ways to draw 7 balls. This gives a probability of 176605/85900584 = 0.00205.., which is about 1 in 500. So this is a rare occurren...
by jaap
Mon Dec 18, 2017 10:49 am
Forum: Number
Topic: Repeating Decimal and Prime Number
Replies: 5
Views: 972

Re: Repeating Decimal and Prime Number

It's a directly follows fermat's little theorem: 10^(p-1) == 1 (mod p) I feel embarrassed to admit: I could not see / understand why 10^(p-1) == 1 (mod p) is the reason, even after reading about introductory number theory in these day. I encounterd some congruences such as "Wilson's theorem" but ye...
by jaap
Sat Oct 28, 2017 10:56 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 223 & 224
Replies: 19
Views: 6378

Re: Problem 223 & 224

I have written 2 pieces of code for problem 223. I get two different answers , for the perimeter limit = 100.000 I get : val1 = 168921 , val2 = 168676 I can't find my code for this problem right now. What you could do is have your computer compare the triangles generated by the two methods until yo...