world:enigmahanoi
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world:enigmahanoi [2020/03/19 17:50] 127.0.0.1 modification externe |
world:enigmahanoi [2022/04/28 14:27] (current) rdouc ↷ Page moved from public:enigmahanoi to world:enigmahanoi |
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| ====== A first illustrative example ====== | ====== A first illustrative example ====== | ||
| - | Two men are sitting in a bar. | ||
| - | > I am bored, man… | + | <note tip>Two different real numbers are in a basket but we don't have access to their values. Pick at random one of them in the basket with equal probabilities and see its value. The question is to find a decision process which allows you to indicate, with a probability strictly larger than $1/2$, which one is the largest . </note> |
| - | >> Then, write two different real numbers on two papers and close them. | + | |
| - | > Done. | + | |
| - | >> I will disclose only one of these papers. And I will tell you with probability strictly larger than 1/2, which paper contains the largest real number. | + | |
| - | > You are kidding! How can you do that? | + | |
| - | + | ||
| - | <note warning>Two different real numbers are in a basket but we don't have access to their values. Pick at random one of them in the basket with equal probabilities and see its value. The question is to find a decision process which allows you to indicate, with a probability strictly larger than $1/2$, which one is the largest . </note> | + | |
| <hidden Answer> $ \newcommand{\rset}{\mathbb R} \newcommand{\PP}{\mathbb P}$ Denote by $X$ the chosen real number that you have in your hand. Let $\alpha: \rset \to (0,1)$ be a (strictly) increasing measurable function. With a probability $\alpha(X)$, say that the largest real number is the one in your hand and otherwise say that this is the one in the basket. | <hidden Answer> $ \newcommand{\rset}{\mathbb R} \newcommand{\PP}{\mathbb P}$ Denote by $X$ the chosen real number that you have in your hand. Let $\alpha: \rset \to (0,1)$ be a (strictly) increasing measurable function. With a probability $\alpha(X)$, say that the largest real number is the one in your hand and otherwise say that this is the one in the basket. | ||
world/enigmahanoi.1584636613.txt.gz · Last modified: 2022/03/16 01:33 (external edit)
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