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#21 EventHorizon

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Posted 21 March 2008 - 03:16 AM

that would probably be right if each orientation possibility had equal probability....but that is not the case. Each of the 49 squares have equal probability. After a square is chosen, then each of it's orientation possibilities have equal probability.


What I meant was that each valid square orientation pair does not have equal probability.....just thought I would fix my horrible wording....
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#22 unreality

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Posted 21 March 2008 - 03:25 AM

Spoiler for how did you weight the average?


Ah yes I'm sorry... I screwed up. I accidentally thought the 4 corners were all 1 instead of two 1's and two 1/2's, so I added on extra small amount which had to make me multiply 49 out to 441 to get a whole number numerator. Gah. I screwed up, I don't know what I was thinking. I had the numbers right but I misread my own handwriting when I was figuring out the averages. :P lol. To see exactly what I did wrong, pretend that the 1/2's adjacent the corners were 1's instead, that's what I read from my handwriting as I calculated the numbers (I did it all in my head), so yeah that came out to 328/441 (441 is 49*9). But yeah :D woops, sorry

the correct answers are then:

Spoiler for Answers (EventHorizon got em all right)


and the interesting thing about #1 and #2:

Spoiler for Interesting thing...

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#23 EventHorizon

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Posted 21 March 2008 - 04:14 AM

and the interesting thing about #1 and #2:

Spoiler for Interesting thing...


That is interesting...it makes me think that perhaps there is a very simple lateral thinking way of solving this puzzle.

I can't quite seem to figure out what it would be yet. I'll think about it more tomorrow...I should really work on a paper...but have been avoiding it a little too much. It seems I would much rather solve puzzles and watch my team lose (grr!) than work on my paper.
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#24 bonanova

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Posted 21 March 2008 - 05:08 AM

Spoiler for method for #1

Posted Image
I think these probabilities apply to a ruler with length 2, not length 3.
Hint: Imagine the ruler begins in the center of a square.
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#25 unreality

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Posted 21 March 2008 - 05:41 PM

bonanova: Yes, 2 spaces long if you want to get picky, if it's from the center of one square to the center of the other, but we practically mean that it covers 3 spaces, the starting space, middle space, and end space. If it started at the middle of each square it would make it 2 spaces long then. If it started at the ends it would make it 3. It starts at the ends ;D and did you see that my 328/441 was incorrect, the chances are 33/49 for white and 16/49 for black (and 79/147 to land on the same color) :P

EventHorizon: yes that's what I was thinking. Maybe it's due to the fact that for a space that can reach less spaces, less spaces can reach that space too. I dunno, I'll think about it some more ;D good luck on your paper!
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#26 unreality

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Posted 22 March 2008 - 05:17 PM

still haven't thought of it...
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