superprismatic
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Everything posted by superprismatic
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Give me a few examples, please. I'm confused about the middle compartment business because I think, at that point, there are 2 things in every compartment. Examples will clear things up.
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I'd be glad to try. I'm not exactly sure of your algorithm, though. Please explain in more detail.
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FOUL! sqrt uses 2 (much like fortieth root uses 40).
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Yes, it made sense. I'm also tired. This will have to wait for 18 hours or so for my attempt to run this thru the program. But I will.
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Sorry, posted to the wrong problem!
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I have a question whose answer will affect the probability. If the host can choose either of the two groups of compartments on either side of your current choice, does he do so randomly? Suppose the winning number is 9 but you chose 4. The host closes 1,2,3. Now, you change your guess to 6. The host may wish to close 7,8 rather than 4,5 to make you think that the 4 that you just abandoned may actually be the winner. This may entice you to go back to 4 later. If he's allowed this kind of shenanigans rather than pick randomly, the probabilities will be affected.
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There is no upper limit to the integers. The OP does specify positive integers, so the lower limit is 1.
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Consider the following two-player game: Each player secretly chooses a positive integer. The integers are revealed simultaneously. The object of the game is to choose an integer which is either exactly one larger than your opponent's integer (in which case, your opponent pays you $2) or which is at least two smaller than your opponent's integer (in which case, your opponent pays you $1). If you both choose the same number, the game is a draw and no money changes hands. So, for example, if A picks 6 and B picks 5, B gives A $2; if A picks 6 and B picks 2, A gives B $1; if A picks 6 and B picks 7, A gives B $2; if A picks 6 and B picks 8, B gives A $1. What is the optimal stratagy for playing this game? Why?
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Oh, now I know how you interpreted the OP. I read it as the +,+,+ rule has to work as well as the +,-,+ one. I guess only KS knows for sure what he meant! Please enlighten us, KS.
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I knew someone would solve it! Nice (but difficult) going! That wraps up the Walter Penney puzzles. You guys solved all of them.
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So do I, but I'm having difficulty proving it.
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