Search results
Results from the WOW.Com Content Network
Banach's match problem is a classic problem in probability attributed to Stefan Banach. Feller [ 1 ] says that the problem was inspired by a humorous reference to Banach's smoking habit in a speech honouring him by Hugo Steinhaus , but that it was not Banach who set the problem or provided an answer.
Suppose l > t.In this case, integrating the joint probability density function, we obtain: = = (), where m(θ) is the minimum between l / 2 sinθ and t / 2 .. Thus, performing the above integration, we see that, when l > t, the probability that the needle will cross at least one line is
The no-three-in-line drawing of a complete graph is a special case of this result with =. [12] The no-three-in-line problem also has applications to another problem in discrete geometry, the Heilbronn triangle problem. In this problem, one must place points, anywhere in a unit square, not restricted to a grid. The goal of the placement is to ...
The aim is to construct a 9-coloring of a particular graph, given a partial 9-coloring. The Sudoku graph has 81 vertices, one vertex for each cell. The vertices are labeled with ordered pairs (x, y), where x and y are integers between 1 and 9. In this case, two distinct vertices labeled by (x, y) and (x′, y′) are joined by an edge if and ...
For each pair of lines, there can be only one cell where the two lines meet at the bottom vertex, so the number of downward-bounded cells is at most the number of pairs of lines, () /. Adding the unbounded and bounded cells, the total number of cells in an arrangement can be at most n ( n + 1 ) / 2 + 1 {\displaystyle n(n+1)/2+1} . [ 5 ]
Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive integers.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
The twelve problems of counting equivalence classes of functions do not involve the same difficulties, and there is not one systematic method for solving them. Two of the problems are trivial (the number of equivalence classes is 0 or 1), five problems have an answer in terms of a multiplicative formula of n and x, and the remaining five ...