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In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties.
A Sudoku with 24 clues, dihedral symmetry (a 90° rotational symmetry, which also includes a symmetry on both orthogonal axis, 180° rotational symmetry, and diagonal symmetry) is known to exist, but it is not known if this number of clues is minimal for this class of Sudoku.
An unsolved Tentai Show puzzle. The same puzzle, solved. The regions are colored to reveal a picture of a cat. Tentai Show (Japanese: 天体ショー tentai shō), also known by the names Tentaisho, Galaxies, Spiral Galaxies, or Sym-a-Pix, is a binary-determination logic puzzle published by Nikoli.
Their symmetry group has two elements, the identity and a diagonal reflection. Z can be oriented in 4 ways: 2 by rotation, and 2 more for the mirror image. It has point symmetry, also known as rotational symmetry of order 2. Its symmetry group has two elements, the identity and the 180° rotation. I can be oriented in 2 ways by rotation.
The most commonly quoted number for the number of possible games, 10 700 [14] is derived from a simple permutation of 361 moves or 361! = 10 768. Another common derivation is to assume N intersections and L longest game for N L total games. For example, 400 moves, as seen in some professional games, would be one out of 361 400 or 1 × 10 1023 ...
The origin of the English word 'tangram' is unclear. One conjecture holds that it is a compound of the Greek element '-gram' derived from γράμμα ('written character, letter, that which is drawn') with the 'tan-' element being variously conjectured to be Chinese t'an 'to extend' or Cantonese t'ang 'Chinese'. [5]
The Key Stage 1, 2 and 3 along with GCSE section covers a range of subjects. In Key Stage 1, 17 subjects are available, including Art and Design, Computing, Design and Technology, English, Geography, History, Maths, Music, Physical Education, PSHE, Citizenship, Religious Education, Science, and Modern Foreign Languages. [5]
Dominos can tile the plane in a countably infinite number of ways. The number of tilings of a 2×n rectangle with dominoes is , the nth Fibonacci number. [5]Domino tilings figure in several celebrated problems, including the Aztec diamond problem in which large diamond-shaped regions have a number of tilings equal to a power of two, [6] with most tilings appearing random within a central ...