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wu :: forums    riddles    hard (Moderators: towr, SMQ, ThudnBlunder, Eigenray, Grimbal, william wu, Icarus)    Random Flying Cards « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Random Flying Cards  (Read 1172 times) fatball Senior Riddler Can anyone help me think outside the box please?     Gender: Posts: 315 Random Flying Cards   « on: Jan 22nd, 2006, 8:53pm » Quote Modify A standard pack of cards is thrown into the air in such a way that each card, independently, is equally likely to land face up or face down.  The total value of the cards which landed face up is then calculated.  (Card values are assigned as follows: Ace=1, ..., King=13.  There are no jokers.)   What is the probability that the total value is divisible by 13? IP Logged Barukh Uberpuzzler     Gender: Posts: 2276 Re: Random Flying Cards   « Reply #1 on: Jan 23rd, 2006, 11:07am » Quote Modify Card throwing probability is a similar problem discussed recently. IP Logged fatball Senior Riddler Can anyone help me think outside the box please?     Gender: Posts: 315 Re: Random Flying Cards   « Reply #2 on: Jan 23rd, 2006, 11:21am » Quote Modify Yes, you are right.  Both partition probability and generating functions  can be used to deal with the problem. IP Logged Eigenray wu::riddles Moderator Uberpuzzler     Gender: Posts: 1948 Re: Random Flying Cards   « Reply #3 on: Jan 24th, 2006, 5:40am » Quote Modify Generalizing to k decks of n cards each, I get 2-kn 1/n [sum]d|n, d odd phi(d) 2kn/d. « Last Edit: Jan 24th, 2006, 6:10am by Eigenray » IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium => hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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