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How to solve puzzles by graphing the rebounds of a bouncing ball: 1963 Oct: About two new and two old mathematical board games 1963 Nov: A mixed bag of problems 1963 Dec: How to use the odd-even check for tricks and problem-solving 1964 Jan: Presenting the one and only Dr. Matrix, numerologist, in his annual performance 1964 Feb
The Tower of Hanoi (also called The problem of Benares Temple, [1] Tower of Brahma or Lucas' Tower, [2] and sometimes pluralized as Towers, or simply pyramid puzzle [3]) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod.
A matchstick puzzle ("Move 1 matchstick to make the equation 6+4=4 valid") and its solution below. Matchstick puzzles are rearrangement puzzles in which a number of matchsticks are arranged into shapes or numbers, and the problem to solve is usually formulated as moving a fixed number of matchsticks to achieve some specific other arrangement.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
The problem is insolvable because any move changes by an even number. Since a move inverts two cups and each inversion changes W {\displaystyle W} by + 1 {\displaystyle +1} (if the cup was the right way up) or − 1 {\displaystyle -1} (otherwise), a move changes W {\displaystyle W} by the sum of two odd numbers, which is even, completing the proof.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The numbers may range from small fractions of 1 to a number the size of a googol (1 followed by a hundred zeroes) or even larger. These slips are turned face down and shuffled over the top of a table. One at a time you turn the slips face up. The aim is to stop turning when you come to the number that you guess to be the largest of the series.
The transformations of the 15 puzzle form a groupoid (not a group, as not all moves can be composed); [12] [13] [14] this groupoid acts on configurations.. Because the combinations of the 15 puzzle can be generated by 3-cycles, it can be proved that the 15 puzzle can be represented by the alternating group. [15]