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2. Water pouring puzzle - Wikipedia

   en.wikipedia.org/wiki/Water_pouring_puzzle

   The simplest solution for 5 liters is (9,0) → (9,8) → (12,5); The simplest solution for 4 liters is (9,0) → (12,0) → (4,8). These solutions can be visualized by red and blue arrows in a Cartesian grid with diagonal lines (of slope -1 such that x + y = c o n s t . {\displaystyle x+y=const.} on these diagonal lines) spaced 4 liters apart ...

3. Eight queens puzzle - Wikipedia

   en.wikipedia.org/wiki/Eight_queens_puzzle

   If the remainder is 3, move 2 to the end of even list and 1,3 to the end of odd list (4, 6, 8, 2 – 5, 7, 9, 1, 3). Append odd list to the even list and place queens in the rows given by these numbers, from left to right (a2, b4, c6, d8, e3, f1, g7, h5). For n = 8 this results in fundamental solution 1 above. A few more examples follow.

4. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...

5. Packing problems - Wikipedia

   en.wikipedia.org/wiki/Packing_problems

   Packing squares in a square: Optimal solutions have been proven for n from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any square integer. The wasted space is asymptotically O(a 3/5). Packing squares in a circle: Good solutions are known for n ≤ 35. The optimal packing of 10 squares in a square

6. Mathematics of Sudoku - Wikipedia

   en.wikipedia.org/wiki/Mathematics_of_Sudoku

   Mathematical context. The general problem of solving Sudoku puzzles on n2 × n2 grids of n × n blocks is known to be NP-complete. [8] A puzzle can be expressed as a graph coloring problem. [9] 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.

7. Mathematical model - Wikipedia

   en.wikipedia.org/wiki/Mathematical_model

   The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...

8. Rhind Mathematical Papyrus - Wikipedia

   en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

   The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057, pBM 10058, and Brooklyn Museum 37.1784Ea-b) is one of the best known examples of ancient Egyptian mathematics. It is one of two well-known mathematical papyri, along with the Moscow Mathematical Papyrus. The Rhind Papyrus is the larger, but younger, of the two..

9. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...