Forum: Science, Math, and Philosophy
12-01-2007, 11:04 AM
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Replies: 4
Views: 899
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>=0.
This can be shown, but is...
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Forum: Science, Math, and Philosophy
12-01-2007, 02:55 AM
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Replies: 4
Views: 899
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Forum: Science, Math, and Philosophy
12-01-2007, 01:01 AM
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Replies: 7
Views: 521
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...
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Forum: Science, Math, and Philosophy
12-01-2007, 12:25 AM
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Replies: 4
Views: 899
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?]}
=...
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Forum: Probability
11-30-2007, 09:50 PM
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Replies: 2
Views: 317
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Forum: Poker Beats, Brags, and Variance
11-30-2007, 03:52 AM
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Replies: 134
Views: 10,592
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? ]
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Forum: Science, Math, and Philosophy
11-29-2007, 07:41 PM
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Replies: 7
Views: 547
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Forum: Science, Math, and Philosophy
11-29-2007, 07:38 PM
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Replies: 7
Views: 547
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Forum: Science, Math, and Philosophy
11-28-2007, 07:54 PM
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Replies: 7
Views: 521
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.
...
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Forum: Science, Math, and Philosophy
11-28-2007, 07:43 PM
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Replies: 7
Views: 521
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Forum: Science, Math, and Philosophy
11-28-2007, 06:36 PM
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Replies: 7
Views: 521
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 ...
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Forum: Science, Math, and Philosophy
11-26-2007, 07:50 PM
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Replies: 24
Views: 1,511
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...
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Forum: Science, Math, and Philosophy
11-25-2007, 09:14 PM
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Replies: 131
Views: 3,567
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>=194) ~
1/5 422 000 000. We should be skeptical of claims of any
IQs >...
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Forum: Science, Math, and Philosophy
11-25-2007, 08:43 PM
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Replies: 22
Views: 854
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...
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Forum: Probability
11-25-2007, 05:11 PM
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Replies: 2
Views: 228
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...
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Forum: Science, Math, and Philosophy
11-25-2007, 12:47 PM
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Replies: 5
Views: 433
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Forum: Probability
11-25-2007, 12:37 PM
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Replies: 2
Views: 207
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...
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Forum: Science, Math, and Philosophy
11-25-2007, 12:16 PM
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Replies: 11
Views: 364
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 >p. [ Take advantage that the difference
between successive...
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Forum: Science, Math, and Philosophy
11-25-2007, 06:47 AM
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Replies: 18
Views: 606
Re: Two Olympiad Problems
The "elliptical idea" seems the most elegant IMO (but I'm
biased since this was the idea that struck immediately).
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Forum: Science, Math, and Philosophy
11-24-2007, 02:05 PM
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Replies: 131
Views: 3,567
Re: Average SMP IQ.
I wrote the Putnam in a year when the problems were easier
than usual (>10 years ago) and regretted not "studying for
it" (amazingly knew hardly any abstract algebra!) and had a
sick feeling...
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Forum: Science, Math, and Philosophy
11-24-2007, 12:59 PM
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Replies: 11
Views: 364
Re: Simple storage problem (math)
This is interesting, but does use the knowledge about the
exact number of primes <2.29 x 10^9, although it's quite
easy to compute.
Without having to compute this (perhaps you simply want to...
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Forum: Science, Math, and Philosophy
11-23-2007, 11:17 PM
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Replies: 131
Views: 3,567
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Forum: Science, Math, and Philosophy
11-23-2007, 01:41 AM
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Replies: 11
Views: 840
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...
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Forum: Science, Math, and Philosophy
11-23-2007, 01:28 AM
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Replies: 11
Views: 364
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...
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Forum: Science, Math, and Philosophy
11-22-2007, 09:08 PM
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Replies: 131
Views: 3,567
Re: Average SMP IQ.
Are there any "legitimate" IQ tests where knowledge or
education in mathematics is NOT going to be helpful?
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