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Post by omaha on Jun 15, 2009 15:41:15 GMT -5
Ok, gotta run to a meeting.
Anyone gets all three of those right, I'll buy you one of whatever you want from John's collection.
Deadline is about an hour from now.
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Post by Deleted on Jun 15, 2009 15:42:03 GMT -5
If anyone likes probability issues, ever hear of the Monte Hall Dillemma? (That one usually stumps math-oriented folks as easily as the rest of us).
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Post by Greg B on Jun 15, 2009 15:47:11 GMT -5
I still can't wrap my head around the Monty Hall problem. But I wrote a Java program to test it and it really does work. I don't understand why, but it does.
OK, Shall we discuss how we solved the first problem? Or should we wait a bit?
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Post by Doug on Jun 15, 2009 15:48:02 GMT -5
If anyone likes probability issues, ever hear of the Monte Hall Dillemma? (That one usually stumps math-oriented folks as easily as the rest of us). I know the answer to that one. "My whole world lies waiting behind, Door Number 3" |
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Post by j on Jun 15, 2009 15:49:07 GMT -5
Even though I solved the initial problem rather quickly, the ones Jeff posted and the sole mention of the Monte Hall dilemma were enough to make me happy with my recent history of math-free higher ed.
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Post by t-bob on Jun 15, 2009 15:55:42 GMT -5
The innumerate English Ph.D. took something over 5 minutes, 4 of them doing addition with a calculator. One, two, three, um, many. Perhaps you were doing addiction with a calculator?  |
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Post by patrick on Jun 15, 2009 16:01:19 GMT -5
In about a minute, used a calculator to check the math.
BActeriology BA
Pathology PhD.
And I really dislike math.
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Post by Greg B on Jun 15, 2009 16:03:07 GMT -5
OK, here's a fun little trick that tickles my Math Geek sensibilities.
I want to add up all the numbers form 1 to [some bigger number] Let's say 1 to 10.
You can do that this way:
N= 1 +2+3+4+5+6+7+8+9+10
Or you can do it this way
N=10+9+8+7+6+5+4+3+2+1
Line them up like this
N= 1 +2 +3 +4 +5 +6 +7 +8 +9 +10
N=10+9 +8 +7 +6 +5 +4 +3 +2 +1
And add the vertical pairs of numbers so you get
11 11 11 11 11 11 11 11 11 11
Add those up and you get 10*11 = 110
But this is twice the number you really wanted. You wanted the sum of 1 to 10 but what we have is the sum of 1 to 10 plus the sum of 10 to 1. So it's twice as much
So divide 110 by 2 and we have 55.
Which means we can do this
1 +2 +3 +4 +5 +6 +7 +8 +9 +10 = 55
Or we can say that ((10 + 1)*10)/2 = 55
HOWEVER, the formula above works for any integer. So the sum of 1 to N is
((N + 1)*N)/2
In computer science we use these kinds of optimizations because to add the sum of 1 to 2345 using the first method would require 2345 additions inside of 2345 iterations of a loop. But using the 2nd method it's just:
((2345 + 1)*2345)/2
and it's done in a single calculation.
These methods are a form of "generating function" where you plug in N and get the Nth result of a series. One of the task we had back in school was to develop a generating function for the Fibonacci series. You pass in a 12 and get the 12th number in the sequence without looping.
Fibonacci , It's as easy as 1 1 2 3
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Post by Russell Letson on Jun 15, 2009 16:05:23 GMT -5
Perhaps you were doing addiction with a calculator? Not addicted, but certainly dependent. |
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Post by millring on Jun 15, 2009 16:17:15 GMT -5
Anyone gets all three of those right, I'll buy you one of whatever you want from John's collection. . I'd just like to point out that I'll be rootin' for y'all. |
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Post by millring on Jun 15, 2009 16:31:30 GMT -5
The innumerate English Ph.D. took something over 5 minutes, 4 of them doing addition with a calculator. One, two, three, um, many. Upon revisiting the thread, I'd just like to say that I love this post. Sincerely, John |
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Post by Russell Letson on Jun 15, 2009 16:37:47 GMT -5
And it's only mildly exaggerated.
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Post by Supertramp78 on Jun 15, 2009 16:41:03 GMT -5
That Monty Hall problem used to drive me up the friggin wall until I wrote it out and ran the odds. damned if it doesn't work. Strangest anti-intuitive piece of math I've ever seen in my life but it is right.
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Post by Greg B on Jun 15, 2009 16:46:42 GMT -5
Here's the results form my Monty Hall program:
Results for shouldSwitch = false
Total Test = 100000
Wins = 33204
Losses = 66796
Results for shouldSwitch = true
Total Test = 100000
Wins = 66765
Losses = 33235
Fully random choice
Total Test = 100000
Wins = 49898
Losses = 50102
If you don't switch you lose 2 out of 3 times. If you do switch then you win 2 out of 3 times (WTF!)
A totally random selection wins about half the time.
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Post by loopysanchez on Jun 15, 2009 16:48:33 GMT -5
Here's one: 0, 1, 2, 6, 21, 110,  ? Just gonna take a guess based on the pattern my brain sees. Is the answer... Scroll down... 777? |
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Post by omaha on Jun 15, 2009 18:14:11 GMT -5
Here's one: 0, 1, 2, 6, 21, 110, ? Just gonna take a guess based on the pattern my brain sees. Is the answer... Scroll down... 777? Good guess, but no. Time's up. The first pattern: The previous number, plus one, multiplied by the Fibonacci number at the same ordinal position. The second pattern : The previous number, plus one, multiplied by the factorial at that ordinal position MINUS the Fibonacci number at the same ordinal position. The third pattern : The ordinal number raised to the power of each integral position of the pi expression (eg, position four = 4^5). So, the next number in series 1 is 888 The next number in series 2 is 27004 The next number in series 3 is 117649 |
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Post by millring on Jun 15, 2009 18:18:39 GMT -5
BRUTby Fibonacci |
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Post by Russell Letson on Jun 15, 2009 18:22:58 GMT -5
I was thinking it was more like "how many fingers am I holding up, divided by the amount of change on Hammond's dresser, plus 6 (in honor of beer), over the square root of cornbread."
To the power of today's date in the Julian calendar.
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Post by Russell Letson on Jun 15, 2009 18:27:44 GMT -5
I was going to use the Brut force method, but I bin sickly.
(Not to be confused with Abu bin Sickly, the Saudi valetudinarian. Or his brother, the salad vegetarian. Or his incontinent great-grandpa, a soiled octogenarian.)
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Post by billhammond on Jun 15, 2009 18:33:26 GMT -5
I was thinking it was more like "how many fingers am I holding up, divided by the amount of change on Hammond's dresser, plus 6 (in honor of beer), over the square root of cornbread." To the power of today's date in the Julian calendar. Russ and Don Peters and I wander off to that faraway poplar grove, mathematically pathetic, but artistically enlightened, at least in our own "minds." And we wield our instruments, and we play and sing. That is our equation, thank you. |
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