@article{(Open Science Index):https://publications.waset.org/pdf/11548,
	  title     = {The Locker Problem with Empty Lockers},
	  author    = {David Avis and  Luc Devroye and  Kazuo Iwama},
	  country	= {},
	  institution	= {},
	  abstract     = {We consider a cooperative game played by n players against a referee. The players names are randomly distributed among n lockers, with one name per locker. Each player can open up to half the lockers and each player must find his name. Once the game starts the players may not communicate. It has been previously shown that, quite surprisingly, an optimal strategy exists for which the success probability is never worse than 1 − ln 2 ≈ 0.306. In this paper we consider an extension where the number of lockers is greater than the number of players, so that some lockers are empty. We show that the players may still win with positive probability even if there are a constant k number of empty lockers. We show that for each fixed probability p, there is a constant c so that the players can win with probability at least p if they are allowed to open cn lockers.
},
	    journal   = {International Journal of Computer and Information Engineering},
	  volume    = {3},
	  number    = {12},
	  year      = {2009},
	  pages     = {2747 - 2750},
	  ee        = {https://publications.waset.org/pdf/11548},
	  url   	= {https://publications.waset.org/vol/36},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 36, 2009},
	}