منابع مشابه
Tied dice
A generalized die is a list (x1; :::; xn) of integers. For integers n 1, a b and s let D(n; a; b; s) be the set of all dice with a x1 ::: xn b and P xi = s. Two dice X and Y are tied if the number of pairs (i; j) with xi < yj equals the number of pairs (i; j) with xi > yj . We prove the following: with one exception (unique up to isomorphism), if X 6= Y 2 D(n; a; b; s) are tied dice neither of ...
متن کاملDice graphs
For integers n 1, a b and s let D(n; a; b; s) be the set of all lists of integers (x1; :::; xn) with a x1 ::: xn b and P xi = s. There is a graph G(n; a; b; s) with vertex-set D(n; a; b; s) in which two vertices are adjacent if one is stronger than the other in a natural dice game. In The prevalence of paradoxical dice [Bull. Inst. Combin. Appl. 45 (2005), 70-76] the dice which are isolated v...
متن کاملSicherman Dice
The subject of Sicherman dice began with a question posed and answered by Colonel George Sicherman which was originally reported in the February 1978 issue of Scientific American. Sicherman wanted to determine if there was another way to label a pair of sixsided dice, using only positive integers such that the probabilities of the sums would be the same as a standard dice. Sicherman discovered ...
متن کاملCertifiable Quantum Dice References Subject Collections Certifiable Quantum Dice
(65 articles) computer modelling and simulation collections Articles on similar topics can be found in the following Email alerting service here in the box at the top right-hand corner of the article or click Receive free email alerts when new articles cite this article-sign up We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n random bits that ...
متن کاملOn the Forged Dice
It is a well{known exercise in elementary probability that it is impossible to forge two ordinary dice with numbers 1;. . .; 6 in such a way that when one throws both and takes the sum one gets the numbers 2; 3;. . .; 12 all with the same probability. preceding assertion is just the statement that for m = 10, k 1 = k 2 = 5 there are no such probabilities. It will be shown how the k 1 ;. . .; k ...
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ژورنال
عنوان ژورنال: ACM SIGARCH Computer Architecture News
سال: 2017
ISSN: 0163-5964
DOI: 10.1145/3140659.3080243