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For those with time left over after turning their old toasters into robots, the awesome magazone Make also has a puzzle section. I particularly enjoyed this one from issue #9:
At one point, a tropical island's population of chameleons was divided as follows:
13 red chameleons
15 green chameleons
17 blue chameleons
Each time two different-colored chameleons would meet, they would change their color to the third one. For example, if green meets red, they both change their color to blue. Is it ever possible for all the chameleons to become the same color?
There's an answer posted on the Make web site, but (spoiler alert!) I took a different, inductive approach that appeals to me a bit more:
Consider an island population of n chameleons at time t of Pt = (Rt, Gt, Bt), where Rt, Gt, and Bt are the number of red, green, and blue chameleons at time t, respectively. We show by induction that if the population consists of n red chameleons, then the population must have always contained an equal number of blue and green chameleons.
Let k = 0 and suppose that at time t = t -k , Rt-k = n = n-2k. Then Gt-k = Bt-k = 0 = 2k. That is, Pt-k = (n,0,0) = (n-2k,k,k).
For k>=0, if Pt-k = (n-2k,k,k), then by the statement of the problem Pt-(k+1) = (n-2(k+1),k+1,k+1). That is, if we have n-2k red chameleons, it must be the case that immediately before we had n-2(k+1) red chameleons and then one green chameleon met one blue chameleon and the two of them changed color to blue, reducing the number of green and blue chameleons from k+1 each to k each.
So, to end up with a population of all red chameleons, we must have started with a population containing an equal number of green and blue chameleons; which we didn't, so we can never end up with all red chameleons.
The argument for why we can't end up with all green or all blue chameleons proceeds the same way.
A lot of friends are geeks, and a lot of them are women. Lately it seems that all the hot geek girls I know are into knitting, crocheting, and the like. Apparently, they're not alone:
Then mathematician Daina Taimina picked up her crochet needles and some synthetic yarn, and the problem was solved. In 1997, Taimina, of Cornell University, found a way to crochet her way into "hyperbolic space." Her woolen creations, which resemble crenulated flowers and hair scrunchies, became the first physical models of the hyperbolic plane.
[via glitterlisa]
Maximum pain is aim of new US weapon, according to the New Scientist. [via alobar]
Requiescat in pace, Ernst Mayr.
Congratulations to the SpaceShipOne team for winning the Ansari X Prize today!
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Stephen Hawking has changed his mind about black holes: "A black hole only appears to form but later opens up and releases information about what fell inside. So we can be sure of the past and predict the future." [via Laporte]
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There are those who say that human brains got big so we could lie better.
Here's an interesting interview with Perry Bartlett of Queensland Brain Institute. It turns out that combing sex, running, and crossword puzzles might be a good way to keep your brain healthy... [via boingboing]
Congratulations to Michael Melvill, who became the first private astronaut in space today. Best wishes to the folks at Scaled Composites in their quest for the X-Prize!
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Break out the sunglasses and don't miss the transit of Venus tomorrow!
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A study of scientific papers published in Nature and the British Medical Journal suggests "a pervasive sloppiness towards statistics in published research".
A belated congratulations to the Civilian Space Exploration Team, who recently reached new heights in amateur rocketry.
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Nature reports that the first accurate sequence of a chimpanzee chromosome suggests that the genetic differences between chimps and humans may be greater than previously thought.
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