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secret codeblack peglower boundbreak secretlog ncodemaker chooseschooses secretcode secondsecond playermastermind wherewhere secretcode queriesupper boundn knecessary breakplayer calledtravelling salesman problemexact queryquery complexitycomplexity yesyes permutationpermutation mastermindmastermind querycomplexity blackpeg mastermindmastermind exactexact heuristicheuristic algorithmsalgorithms travellingtravelling salesmansalesman problemproblem multiplemultiple timetime windowswindows hotelhotel selectionselection mastermindmastermind famousfamous playerplayer gamegame playerplayer codemakerplayer codebreakercodebreaker supposedsupposed crackcrack minimumminimum numbernumber codecode guessesguesses queriesqueries codemakercodemaker dutyduty helphelp codebreakercodebreaker providingproviding defineddefined errorerror measuremeasure secretcode guessedguessed codecode queryquery considerconsider variantvariant calledcalled yesqueries repetitioninformation codemakerposition mastermindk≥n colorscolors ℓℓ kk −n−n provebound kjkj ℓlogℓlog upperbound nlognlog nk numberqueries necessaryrepresent permutationsΘ nlognmastermind players
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