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April 24th, 2006, 8:17 pm
Forum: Brainteaser Forum
Topic: Alternating harmonic sum
Replies: 85
Views: 119200

### Alternating harmonic sum

Nevermind.. just realized my "proof" is erroneous. Needs more work on the numerator...
April 24th, 2006, 8:13 pm
Forum: Brainteaser Forum
Topic: Alternating harmonic sum
Replies: 85
Views: 119200

### Alternating harmonic sum

Sorry, meant 1335!
April 24th, 2006, 7:55 pm
Forum: Brainteaser Forum
Topic: Alternating harmonic sum
Replies: 85
Views: 119200

### Alternating harmonic sum

2003 is prime. Multiply numerator and denominator by 2003!, you get that the denominator is not divisible by 2003, and the numerator is a sum of terms of the form (-1)^k 2003!/k, where k<=1335. All of these terms are divisible by 2003, hence the numerator is divisible by 2003. QED.
March 8th, 2006, 2:36 pm
Forum: Brainteaser Forum
Topic: circle covering
Replies: 36
Views: 159854

### circle covering

<t>QuoteOriginally posted by: beatlemaniaQuoteOriginally posted by: mattcushmanIf we can find a non-negative function f(x,y) such that the integral of f(x,y) over any strip intersected with the circle is equal to A, while f(x,y) integrated over the whole circle is B with B > 9A, we are done.Can you ...
July 8th, 2005, 1:44 pm
Forum: Brainteaser Forum
Topic: programming teasers - Part 2 -- Sort and Search
Replies: 1
Views: 143590

### programming teasers - Part 2 -- Sort and Search

You can find the value of X in O(log N) time (essentially a binary search, you keep narrowing down the position by a factor of 2 with each test by starting with a=1, b=N, so x(a)>x(b) [unless X=0] and bisect). From there, you can use a plain vanilla binary search, also O(log N).
July 1st, 2005, 6:19 pm
Forum: Off Topic
Topic: Neuro Electromagnetic weapons
Replies: 121
Views: 180015

### Neuro Electromagnetic weapons

Amin,Can you describe some of your research? I take it you don't work in fixed income. It sounds very important to have generated this sort of interest at the highest levels of the government.
July 1st, 2005, 9:26 am
Forum: Off Topic
Topic: Number of lurkers in OffTopic is quite astounding...
Replies: 11
Views: 144344

### Number of lurkers in OffTopic is quite astounding...

<t>QuoteOriginally posted by: fars1d3sThe reason it's "astounding" as you say, is because this section has so many interesting and compelling topics. It's almost addictive, because it draws out all the curiosity in you. There are some very good arguments and discussions on here. People want to find ...
June 29th, 2005, 6:27 pm
Forum: Off Topic
Topic: America's Religious Right
Replies: 45
Views: 145487

### America's Religious Right

<t>QuoteOriginally posted by: farmerQuoteOriginally posted by: mattcushmanYou seem to suffer from some compulsion to spew convolved justifications for your beliefs. Tell me, is it insecurity?It's mdubuque. He asked me the same question three times, like he really cared and didn't understand my answe...
June 29th, 2005, 6:00 pm
Forum: Off Topic
Topic: America's Religious Right
Replies: 45
Views: 145487

### America's Religious Right

<t>farmer,Your answers are clearly disingenuous. You claim parents have to be informed of a minor's abortion to preserve the rights of the parents (the right of the parents to preserve the rights of the minor child... it's all for the child's sake, of course). You are also against the morning after ...
June 21st, 2005, 4:27 pm
Forum: Brainteaser Forum
Topic: 5 equivalence classes
Replies: 4
Views: 145360

### 5 equivalence classes

<t>Use the fact that, mod 13, the integers are a field with the multiplicative group being cyclic of order 12. Thus, the cubes yield 4 distinct elements of Z/(13). Add in 0, and you get 5 distinct powers of 3 in Z/(13). So, defined x~y to mean X^3 = Y^3 (mod 13).Explicitly, these equivalence classes...
May 4th, 2005, 7:58 pm
Forum: General Forum
Topic: CAPM and sector dependence
Replies: 14
Views: 151913

### CAPM and sector dependence

<t>One common misunderstanding of CAPM is that people think it's a one factor model in the sense that all inter-correlations of stocks are given by their correlations with the market as a whole. Is this what you mean by "critique"?Actually, CAPM allows for the residual "specific" risks to be correla...
April 28th, 2005, 5:36 pm
Forum: Brainteaser Forum
Topic: circle covering
Replies: 36
Views: 159854

### circle covering

I tried a bunch of solutions along those lines, playing with both arc length and area. The solution I gave below is in a way inspired by those, but I needed to use this funny area w.r.t a different measure to get it to work.
April 6th, 2005, 2:40 pm
Forum: Brainteaser Forum
Topic: circle covering
Replies: 36
Views: 159854

### circle covering

Chiron,Optimal in what sense? Why is this true, but only when the total width is less than the diameter? These statements are not obvious. I don't see how you have supplied a proof of anything.I'm doubtful that there is a shorter proof than mine, but would love to see one.
April 5th, 2005, 3:42 pm
Forum: Brainteaser Forum
Topic: circle covering
Replies: 36
Views: 159854

### circle covering

<t>They can overlap in principle, but not in practice. I still don't follow your alleged proof.OK, let me ask you this then... applying your math with 10 strips, it seems that you can actually prove that 10 strips doesn't work either, as 2R*sin(pi/10)>1 as well. So, do you agree that you cannot do i...
April 5th, 2005, 3:11 pm
Forum: Brainteaser Forum
Topic: circle covering
Replies: 36
Views: 159854

### circle covering

<t>chiron,I don't see a proof there. Anyway, the most efficient way to cover the circle be to use strips side by side, and not arranged in any sort of polygon. That's the only way you can do it with 10 strips, as a simple extension of the proof below actually shows. There can be no overlap in the st...
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