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Forum: Science, Math, and Philosophy 12-01-2007, 11:04 AM
Replies: 4
Views: 62
Posted By bigpooch
Re: Hyperfactorial Problem

Okay, the problem is equivalent to showing:
<font color="white">
C(x+b,b)C(x+b+1,b)...C(x+b+m,b) is divisible by
C(b,b)C(b+1,b)...C(b+m,b) for any integer x&gt;=0.

This can be shown, but is...
Forum: Science, Math, and Philosophy 12-01-2007, 02:55 AM
Replies: 4
Views: 62
Posted By bigpooch
Re: Hyperfactorial Problem

Ignore my last post!
Forum: Science, Math, and Philosophy 12-01-2007, 01:01 AM
Replies: 7
Views: 38
Posted By bigpooch
Re: An original math problem

Basically, pzhon answered it all but he wasn't explicit
about 4):

<font color="white">
A very rough approximation for the EV of the game for
general n is sqrt(pi*n) - 8 (including the $7 fee...
Forum: Science, Math, and Philosophy 12-01-2007, 12:25 AM
Replies: 4
Views: 62
Posted By bigpooch
Re: Hyperfactorial Problem

Isn't this "superfactorical" instead?

Answer:
<font color="white">
(m+n)?/m? = (m+n-1)!...m!

f(a,b,c) = [(a+b+c)?/(a+b)?]c?/{[(a+c)?/a?][(b+c)?/b?]}
=...
Forum: Probability 11-30-2007, 09:50 PM
Replies: 2
Views: 21
Posted By bigpooch
Re: 7 Card stud, who wants to do the math for me???

Not all correct. There are 4 combinations of KKK out of
C(52,3)= 22 100; therefore, the probability is 1/5525.
So getting KKK and then AAA is exactly 1/30 525 625 (this
part is correct).
...
Forum: Poker Beats, Brags, and Variance 11-30-2007, 03:52 AM
Replies: 134
Views: 185
Posted By bigpooch
Re: $43 million error at Party (screenshot)

Actually, it is 2^32 - 1 cents. If the OP had won $0.01
before contacting PartyPoker, his balance might become
zero. [ I don't think anyone can have a negative balance,
right? ]
Forum: Science, Math, and Philosophy 11-29-2007, 07:41 PM
Replies: 7
Views: 21
Posted By bigpooch
Re: Antiderivative problem

d/dx(ln(ax+b)) = a/(ax+b)

so d/dx(1000/3 ln(3x+1)) = 1000/(3x+1)
Forum: Science, Math, and Philosophy 11-29-2007, 07:38 PM
Replies: 7
Views: 21
Posted By bigpooch
Re: Antiderivative problem

You mean

1000x
-------
x^2 + 16

for the last one.

Hint: d/dx (ln u) = (du/dx)/u
Forum: Science, Math, and Philosophy 11-28-2007, 07:54 PM
Replies: 7
Views: 38
Posted By bigpooch
Re: An original math problem

<font color="white">
A simple arithmetic error in 3): if you get 30 right
(approximately what you'd expect when the deck evens out 8
times), excluding the fee, the gain is $30-$22 = $8.
...
Forum: Science, Math, and Philosophy 11-28-2007, 07:43 PM
Replies: 7
Views: 38
Posted By bigpooch
Re: An original math problem

It was your post on SMP that inspired me to post this
problem; it's helpful for part 3).
Forum: Science, Math, and Philosophy 11-28-2007, 06:36 PM
Replies: 7
Views: 38
Posted By bigpooch
An original math problem

This is related to a recent post on SMP.

The "proposition"
----------------

You pay $7 for the privilege of playing this game with an
ordinary deck of cards: 26 red cards and 26 black. You ...
Forum: Science, Math, and Philosophy 11-26-2007, 07:50 PM
Replies: 24
Views: 29
Posted By bigpooch
Re: Maths problem

For the RHS of the recurrence is 4^n, the solution is
combinatorial. Are you suggesting techniques or methods
that are useful in the general case: where the RHS = g(n)
(even simply if g(n)=b^n...
Forum: Science, Math, and Philosophy 11-25-2007, 09:14 PM
Replies: 131
Views: 92
Posted By bigpooch
Re: Average SMP IQ.

Pretty close.

I don't want to sound like a nit, but if IQs are normally
distributed with mean 100 and SD = 15, prob(IQ&gt;=194) ~
1/5 422 000 000. We should be skeptical of claims of any
IQs &gt;...
Forum: Science, Math, and Philosophy 11-25-2007, 08:43 PM
Replies: 22
Views: 20
Posted By bigpooch
Re: Define Intelligence.

From http://en.wikipedia.org/wiki/Intelligence:

[ The neutrality of this article is disputed. ]

The definition of intelligence has long been a matter of controversy.

Intelligence comes from...
Forum: Probability 11-25-2007, 05:11 PM
Replies: 2
Views: 26
Posted By bigpooch
Re: Combinatorics messing with me...

You are overcounting the situations where you receive more
than one of the two key cards. Of the C(49,4)=211876
combinations, you get these number of combinations for:

2 key cards: 4 x 4 x...
Forum: Science, Math, and Philosophy 11-25-2007, 12:47 PM
Replies: 5
Views: 21
Posted By bigpooch
Re: Quick Math Question - Lagrangian

You mean "Lagrange Multipliers"; link:

http://en.wikipedia.org/wiki/Lagrange_multipliers
Forum: Probability 11-25-2007, 12:37 PM
Replies: 2
Views: 33
Posted By bigpooch
Re: Probability of Flush Given 3 clubs on flop

Seems right:

P(first player has flush) = C(10,2)/C(49,2) = 45/1176
P(1st and 2nd player has flush) = [C(10,2)/C(49,2)][C(8,2)/C(47,2)] ~ 0.0009911457645 (call this p)
P(1st, 2nd and 3rd player...
Forum: Science, Math, and Philosophy 11-25-2007, 12:16 PM
Replies: 11
Views: 14
Posted By bigpooch
Re: Simple storage problem (math)

This is a worthwhile idea to consider. Define g(p) to be a
"modified gap" function g(p) = (q-p-2)/2 where q is the
least prime &gt;p. [ Take advantage that the difference
between successive...
Forum: Science, Math, and Philosophy 11-25-2007, 06:47 AM
Replies: 18
Views: 26
Posted By bigpooch
Re: Two Olympiad Problems

The "elliptical idea" seems the most elegant IMO (but I'm
biased since this was the idea that struck immediately).
Forum: Science, Math, and Philosophy 11-24-2007, 02:05 PM
Replies: 131
Views: 92
Posted By bigpooch
Re: Average SMP IQ.

I wrote the Putnam in a year when the problems were easier
than usual (&gt;10 years ago) and regretted not "studying for
it" (amazingly knew hardly any abstract algebra!) and had a
sick feeling...
Forum: Science, Math, and Philosophy 11-24-2007, 12:59 PM
Replies: 11
Views: 14
Posted By bigpooch
Re: Simple storage problem (math)

This is interesting, but does use the knowledge about the
exact number of primes &lt;2.29 x 10^9, although it's quite
easy to compute.

Without having to compute this (perhaps you simply want to...
Forum: Science, Math, and Philosophy 11-23-2007, 11:17 PM
Replies: 131
Views: 92
Posted By bigpooch
Re: Average SMP IQ.

FWIW:

My raw score on the only Putnam I wrote was in the 70s.
Forum: Science, Math, and Philosophy 11-23-2007, 01:41 AM
Replies: 11
Views: 25
Posted By bigpooch
Re: A Putnam Geometry Problem

Was this really on the Putnam? [seems too easy]

Answer:

<font color="white">
Such a rectangle must be able to hold two squares of side
1/sqrt(2), so it has to have length AT LEAST twice...
Forum: Science, Math, and Philosophy 11-23-2007, 01:28 AM
Replies: 11
Views: 14
Posted By bigpooch
Re: Simple storage problem (math)

Not quite, but you are on the right track.

Out of the integers between 7 and n, 1/2 are not divisible
by 2, (1/2)(2/3) = 1/3 are not divisible by 2 or 3, and
(1/2)(2/3)(4/5) = 4/15 are not...
Forum: Science, Math, and Philosophy 11-22-2007, 09:08 PM
Replies: 131
Views: 92
Posted By bigpooch
Re: Average SMP IQ.

Are there any "legitimate" IQ tests where knowledge or
education in mathematics is NOT going to be helpful?
Showing results 1 to 25 of 479

 
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