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In combinatorics, stars and bars (also called "sticks and stones", [1] "balls and bars", [2] and "dots and dividers" [3]) is a graphical aid for deriving certain combinatorial theorems. It can be used to solve a variety of counting problems , such as how many ways there are to put n indistinguishable balls into k distinguishable bins. [ 4 ]
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The first pentathlon was documented in Ancient Greece and was part of the Ancient Olympic Games. Five events were contested over one day for the Ancient Olympic pentathlon , starting with the long jump , javelin throwing , and discus throwing , followed by the stadion (a short foot race) and wrestling .
The Academic Pentathlon (USAP) is an academic competition involving five academic fields of study (math, social sciences, science, literature, and fine arts). It is run by the USAD (United States Academic Decathlon) . [ 1 ]
The symmetrical arrangement of the stars on the American flag and related matters 1976 Sep: John Horton Conway's book covers an infinity of games 1976 Oct: Combinatorial problems, some old, some new and all newly attacked by computer 1976 Nov: In which DM (Dr. Matrix) is revealed as the guru of PM (Pentagonal Meditation) 1976 Dec
Stars and Bars (flag), the first (1861–1863) flag of the Confederate States of America; Stars and Bars, 1988 comedy starring Daniel Day-Lewis; Stars and Bars, 1917 silent film comedy directed by Victor Heerman; Stars and bars (combinatorics), a graphical method used to derive the formula for multiset coefficients and other combinatorial theorems
This sounds like the premise of a superhero movie: A college dropout suffered a serious head injury after being mugged -- and came out a genius. 43-year-old Jason Padgett was knocked unconscious ...
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.