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The power of 3 multiplying a is independent of the value of a; it depends only on the behavior of b. This allows one to predict that certain forms of numbers will always lead to a smaller number after a certain number of iterations: for example, 4a + 1 becomes 3a + 1 after two applications of f and 16a + 3 becomes 9a + 2 after four applications ...
The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 2 64 −1 or 18,446,744,073,709,551,615 (eighteen quintillion ...
Voronoi diagram. In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called ...
The Ages of Three Children puzzle (sometimes referred to as the Census-Taker Problem[1]) is a logical puzzle in number theory which on first inspection seems to have insufficient information to solve. However, with closer examination and persistence by the solver, the question reveals its hidden mathematical clues, especially when the solver ...
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and ...
In botany, a seed is a plant embryo and food reserve enclosed in a protective outer covering called a seed coat (testa). More generally, the term "seed" means anything that can be sown, which may include seed and husk or tuber. Seeds are the product of the ripened ovule, after the embryo sac is fertilized by sperm from pollen, forming a zygote.
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