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Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators. The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property.
Mathematical puzzles require mathematics to solve them. Logic puzzles are a common type of mathematical puzzle. Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions. After these conditions are set ...
The largest puzzle (40,320 pieces) is made by a German game company Ravensburger. [8] The smallest puzzle ever made was created at LaserZentrum Hannover. It is only five square millimeters, the size of a sand grain. The puzzles that were first documented are riddles. In Europe, Greek mythology produced riddles like the riddle of the Sphinx ...
Cengage Learning filed for bankruptcy under Chapter 11 on July 2, 2013. [22] [27] Cengage Learning emerged from bankruptcy on April 1, 2014, eliminating approximately $4 billion of its funded debt and securing $1.75 billion in exit financing. Post-bankruptcy, the company decided to focus on developing digital study guides and other educational ...
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Example grid for a cross-figure puzzle with some answers filled in. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells.
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