The Dice Club Project

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.

“Why are you repeatedly throwing that die, Vince, won’t you get a sore arm,” asked Jack.

“Hope not. I’m checking how many throws are needed to get all die faces from one to six to appear at least once,” said Vince.

“Any conclusion so far?” asked Jack.

“Seems that about 14 throws will do the job,” said Vince, after checking some marks on a notepad. “We’re running a project to check the results for different numbers of dice,” added Vince.

“So you’ll soon be using two dice to see how many throws are needed to get all the doubles?” said Jack.

“That’s the next step,” agreed Vince, “probably take quite a bit longer. Maybe I’ll pass the job on to Joe over there,” said Vince, rubbing his elbow.

“Charlie at the big table yonder is working on getting all the triples, but he’s been at it for a really long time,” said Vince.

“Anybody working out the probability for n dice?” said Jack.

“Yeah, my cousin Lennie at the desk over there is doing the theory and checking it out on a PC. He’s quite good at math,” said Vince.

“Good luck with the project, Vince. Seems a bit complicated to me, so I’ll be heading for the lounge,” said Jack.

Can you offer a formula for calculating the number of throws with n dice needed to get all the n-tuples?

 

About Ken

Bachelor of Science in Physics, Honors, University of Maryland. Graduate of Danish School of Classical Homeopathy in 1998. Studies over several years at the International Academy of Classical Homeopathy in Alonnisos, Greece with the world-famous homeopath George Vithoulkas (winner of the Right Livelihood Award, the alternative Nobel Prize). Director of Klinik for Klassisk Homøopati in Herlev, Denmark. Director of the Iberian School and Clinic of Classical Homeopathy in Estepona, Costa del Sol, Spain and Gibraltar. Founding member of the Spanish Association of Classical Homeopathy (Asociación Española de Homeopatía Unicista) approved by ECCH (European Council for Classical Homeopathy). Currently director of the International Homeopathic Web Clinic and the Avila Clinic and School of Classical Homeopathy in Caracas, Venezuela. Kjetill Oftedal offers consultations in English, Spanish, Norwegian, Danish, Swedish, German, Dutch and Portuguese.
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