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A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average .
The most common problem being solved is the 0-1 knapsack problem, which restricts the number of copies of each kind of item to zero or one. Given a set of items numbered from 1 up to , each with a weight and a value , along with a maximum weight capacity ,
For example, in detecting a dissimilar coin in three weighings ( = ), the maximum number of coins that can be analyzed is = .Note that with weighings and coins, it is not always possible to determine the nature of the last coin (whether it is heavier or lighter than the rest), but only that the other coins are all the same, implying that the last coin is the ...
Coin values can be modeled by a set of n distinct positive integer values (whole numbers), arranged in increasing order as w 1 through w n.The problem is: given an amount W, also a positive integer, to find a set of non-negative (positive or zero) integers {x 1, x 2, ..., x n}, with each x j representing how often the coin with value w j is used, which minimize the total number of coins f(W)
In mathematics, the coin problem (also referred to as the Frobenius coin problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks for the largest monetary amount that cannot be obtained using only coins of specified denominations. [1]
By the time that the fifth square is reached on the chessboard, the board contains a total of 31, or , grains of wheat.. The wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as:
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.
(B) (,) of weight = and minimal order exist if is a prime power and such a circulant weighing matrix can be obtained by signing the complement of a finite projective plane. Since all C W ( n , k ) {\displaystyle CW(n,k)} for k ≤ 25 {\displaystyle k\leq 25} have been classified, the first open case is C W ( 105 , 36 ) {\displaystyle CW(105,36)} .