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Talk:Eight options with six sides

1,207 bytes added, 20:40, 23 December 2010
This seems too easy
== This seems too easy ==
Determining the <i>least</i> number of rolls he <i>will</i> have to make is so trivial I wouldn't even call it a puzzle. Determining the <i>greatest</i> number of rolls he <i>may</i> have to make is a slightly less trivial, but still very simple. One can optimise either of these values or both of them. Perhaps one for [[:Category:Easy puzzles]]?
As far as I can tell, I'm not missing anything. [[User:Zerrakhi|Zerrakhi]] 03:43, 22 October 2010 (EDT)
: Hmmm. I'm not seeing this as easy. Perhaps I am missing something. That or I worded the question in an unclear way. Could you tell me what you think the answer is? That would help me understand what is going on here. [[User:Oscarlevin|Oscarlevin]] 15:03, 18 November 2010 (EST)
 
:: '''To optimise the LEAST number of rolls he WILL have to make:'''
 
:: Let N be the least integer such that 6^N >= D where D is the number of dishes.
:: Of the 6^N possible permutations of rolled numbers, allocate a certain number to each dish and leave the rest blank.
:: The number of permutations allocated to each dish is the greatest integer A such that A <= (6^N)/D.
:: Roll N dice. If the permutation that's rolled is allocated a dish, select that dish. Otherwise roll again.
:: With this method, an infinite number of rolls MAY be needed, but the least number of rolls that WILL be needed is simply N.
:: If D = 8 then N = 2 and A = 4.
 
:: '''To optimise the MOST number of rolls he MAY have to make:'''
 
:: Let N be the least integer such that 6^N is a multiple of D.
:: Allocate permutations arbitrarily to dishes, as above except that now every permutation is allocated a dish (there are no blank spaces).
:: With this method, exactly N rolls are needed, no more no less.
:: If D = 8 then N = 3 and A = 27 (because 6 ^ 3 = 8 * 27).
:: The least easy bit is characterising the values of D such that N exists, but that's not part of the main puzzle.
 
:: [[User:Zerrakhi|Zerrakhi]] 21:40, 23 December 2010 (EST)
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