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| ==A coin puzzle==
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| [http://wordplay.blogs.nytimes.com/2014/03/17/coin/?module=BlogPost-Title&version=Blog%20Main&contentCollection=Numberplay&action=Click&pgtype=Blogs®ion=Body A coin problem]<br>
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| by Gary Antonik, Numberplay blog, ''New York Times'', 17 March 2014
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| The post begins with this simple problem, posed by Daniel Finkel:
| | ==Numbers with painting== |
| <blockquote>
| | Bob Griffin sent a link to: |
| Consider this simple game: flip a fair coin twice. You win if you get two heads, and lose otherwise. It’s not hard to calculate that the chances of winning are 1/4… . Your challenge is to design a game, using only a fair coin, that you have a 1/3 chance of winning.
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| </blockquote>
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| Continues "And here is my recipe for getting the most out of this problem: if you can solve it, do not stop with one answer. Rather, see how many answers you can come up with. I’ve posed this problem to many people, and I continue to hear novel solutions."
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| Here are three ways that suggested themselves (I notice they also had soon showed up in readers' comments to the ''NYT''!):
| | [http://fivethirtyeight.com/features/a-statistical-analysis-of-the-work-of-bob-ross/ A statistical analysis of the work of Bob Ross]<br> |
| * Toss the coin until the first head appears. You win if this takes an even number of tosses
| | by Walt Hickey, FiveThirtyEightLife blog, 14 April 2014 |
| * Toss the coin twice. You win on HH and lose on HT or TH. If TT appears, ignore the result and make another two tosses.
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| * Toss the coin until the first appearance of HTT or HHT on consecutive tosses. You win HTT.
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| The third is an instance of the game [http://en.wikipedia.org/wiki/Penney's_game Penney-Ante], invented by William Penney. It is a famous example of non-transitivity: whatever triple you choose, I can choose one that has a better than even chance of coming up first. What I did not know until I searched for this online description, was that there is a known variation with cards, called the [http://en.wikipedia.org/wiki/Penney's_game#Variation_with_playing_cards Humble-Nishiyama Randomness Game]
| | Ross was painter on the PBS series, “The Joy of Painting." He starred in 403 episodes that originally aired from 1983-1994, and are still showing in reruns. |
| | The blog post give the following graphic showing how often various elements appeared in Ross's pairings. |
| | : [[File:Hickey-ross.png | 389px]] |
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| | | To be continued... |
| Submitted by Bill Peterson
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Numbers with painting
Bob Griffin sent a link to:
A statistical analysis of the work of Bob Ross
by Walt Hickey, FiveThirtyEightLife blog, 14 April 2014
Ross was painter on the PBS series, “The Joy of Painting." He starred in 403 episodes that originally aired from 1983-1994, and are still showing in reruns.
The blog post give the following graphic showing how often various elements appeared in Ross's pairings.
To be continued...
