One Saturday afternoon, as Jack, a new member, entered the Snake Eyes Dice Club he saw many people busy throwing dice at various felt-covered tables.<\/p>\n
\u201cWhy are you repeatedly throwing that die, Vince, won\u2019t you get a sore arm,\u201d asked Jack.<\/p>\n
\u201cHope not. I\u2019m checking how many throws are needed to get all die faces from one to six to appear at least once,\u201d said Vince.<\/p>\n
\u201cAny conclusion so far?\u201d asked Jack.<\/p>\n
\u201cSeems that about 14 throws will do the job,\u201d said Vince, after checking some marks on a notepad. \u201cWe\u2019re running a project to check the results for different numbers of dice,\u201d added Vince.<\/p>\n
\u201cSo you\u2019ll soon be using two dice to see how many throws are needed to get all the doubles?\u201d said Jack.<\/p>\n
\u201cThat\u2019s the next step,\u201d agreed Vince, \u201cprobably take quite a bit longer. Maybe I\u2019ll pass the job on to Joe over there,\u201d said Vince, rubbing his elbow.<\/p>\n
\u201cCharlie at the big table yonder is working on getting all the triples, but he\u2019s been at it for a really long time,\u201d said Vince.<\/p>\n
\u201cAnybody working out the probability for n dice?\u201d said Jack.<\/p>\n
\u201cYeah, my cousin Lennie at the desk over there is doing the theory and checking it out on a PC. He\u2019s quite good at math,\u201d said Vince.<\/p>\n
\u201cGood luck with the project, Vince. Seems a bit complicated to me, so I\u2019ll be heading for the lounge,\u201d said Jack.<\/p>\n
Can you offer a formula for calculating the number of throws with n dice needed to get all the n-tuples?<\/em><\/p>\n \u00a0<\/em><\/p>\nShare this:<\/h3>