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# plasmid

Member Since --
Offline Last Active Jun 17 2015 03:38 AM

### #338643Four-legged stool

Posted by on 17 June 2014 - 03:35 PM

Spoiler for

Edit: This assumes that the legs of the stool form a square. Determining whether it applies if the legs are in any other orientation is left as an exercise for the reader.
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### #338586The "aha!" problems 5. Four-point square

Posted by on 07 June 2014 - 03:52 AM

If lines AC and BD are perpendicular and of different length, then line D-D' will not have two different perpendiculars with one going through A and one going through C... both perpendiculars will emanate from the same point. So in the end it wouldn't really describe a square so much as a point whose "edges" if extended would touch each of the four points.

But I do think your solution is far more Aha-y.
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### #338371Riffle Shuffle

Posted by on 19 May 2014 - 04:04 AM

Spoiler for

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### #337817Random number probability

Posted by on 16 March 2014 - 04:45 PM

Spoiler for

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### #337779collatz sequence^2

Posted by on 13 March 2014 - 04:17 PM

The thing I still don't understand is whether or not you can prove that you've got a set of generating functions that will cover all numbers that will converge. That's why I took the different approach of starting at the number 1 and applying the algorithm backwards -- if you can cover all cases that can be reached by working from 1 backwards then you know you've covered every number that converges, so any number not on that list can't converge. I just can't come up with an adequate way to show definitively that I've covered all generating functions of the form
(n x 2a + 1) x 2b
by finding all values of n using the function
sqrt(n x 2a + 1) = next value of n

In fact I know I'm missing some numbers that do converge, maybe because the generating function behaves strangely at higher values or something, because my approach didn't pick up that 47, 93, and 185 converge using the list of numbers generated in the previous perl program. (Either that or maybe rounding errors are making my computer miss whether it's dealing with integers or not after taking log base 2.)

If you want to make a list of numbers that your functions cover, you could compare it to the list of the numbers from 1 to 200 that appear to diverge: 27, 39, 43, 51, 53, 55, 59, 71, 45, 77, 79, 83, 85, 87, 91, 95, 99, 101, 103, 105, 107, 109, 111, 115, 117, 119, 123, 135, 139, 141, 143, 147, 149, 151, 153, 155, 157, 159, 163, 165, 167, 169, 171, 173, 175, 179, 181, 183, 187, 189, 191, 195, 197, 199 and multiples of powers of two for each of those.
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### #337660Bake it

Posted by on 02 March 2014 - 05:26 PM

If the pieces of cake must have the same size and shape, then I get the feeling this isn't one of those questions of the "one person cuts and another chooses" variety. It's asking how a certain number of slices can result in equally shaped pieces if the guests can cut with absolute precision.

Spoiler for if that's the case, perhaps this is what you're getting at?

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### #337345The Magnetized Coin

Posted by on 08 February 2014 - 05:42 PM

Spoiler for Solution with one weighing

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### #337047Food For Thought

Posted by on 20 December 2013 - 05:46 AM

Spoiler for revised poke at the first

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### #336891Food For Thought

Posted by on 04 December 2013 - 08:53 AM

Getting things started, for
Packs quite a wallop, when one really sings
Motions to give the shaft, certain body rings
Spoiler for I'd say
I'll have to take it up a notch to make a decent try at the others.
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### #336004A Brief Diversion

Posted by on 01 October 2013 - 04:25 AM

Spoiler for

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### #335991blind bartender

Posted by on 30 September 2013 - 04:34 AM

Very neat problem. The answer is certainly unintuitive.
Spoiler for Checkmate in 7

Edit: renamed states for clarity
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### #333404June 2013 ROM - Word-Riddle-of-the-Month - I'm not a siren

Posted by on 21 June 2013 - 05:24 AM

Never underestimate the Dude.
Hopefully the imagery of the riddle is obvious to all after seeing the answer.
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Posted by on 18 June 2013 - 07:31 AM

With a little bit of magical sleight-of-letter:
Spoiler for

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### #333200June 2013 ROM - Word-Riddle-of-the-Month - I'm not a siren

Posted by on 16 June 2013 - 04:24 PM

Bloodthirsty tongues, coated sweet
Welcoming mats on the floors
Lost in their dream, thus I greet
Then wake with a crack at the boards
Metal and wood, right and left
Crashing, they pray to take flight
Fully renounce plan of theft
For life or for death clinging tight
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### #330601Fowl Play

Posted by on 13 April 2013 - 06:19 PM

Spoiler for Flustered and showed the way out

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