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The 5×5 board was weakly solved for all opening moves in 2002. [32] The 7×7 board was weakly solved in 2015. [33] Humans usually play on a 19×19 board, which is over 145 orders of magnitude more complex than 7×7. [34] Hex A strategy-stealing argument (as used by John Nash) shows that all square board sizes cannot be lost by the first player ...
The V-Cube 7 is a combination puzzle in the form of a 7×7×7 cube. The first mass-produced 7×7×7 was invented by Panagiotis Verdes and is produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a number of Chinese companies, [ 1 ] some of which have mechanisms which improve on the original.
However, draughts with only 5 × 10 20 positions [21] and even fewer, 3.9 × 10 13, in the database, [22] is a much easier problem to solve –of the same order as Rubik's cube. The magnitude of the set of positions of a puzzle does not entirely determine whether a God's algorithm is possible.
Lastly the four rhomboids that form elongated crosses also give the magic sum: 23+1+9+24+8, 15+1+17+20+12, 14+1+18+13+19, 7+1+25+22+10. Such squares with 1 at the center cell are also called God's magic squares in Islamic amulet design, where the center cell is either left blank or filled with God's name.
The mutilated chessboard problem is an instance of domino tiling of grids and polyominoes, also known as "dimer models", a general class of problems whose study in statistical mechanics dates to the work of Ralph H. Fowler and George Stanley Rushbrooke in 1937. [1]
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Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations In mathematics , a multiplication table (sometimes, less formally, a times table ) is a mathematical table used to define a multiplication operation for an algebraic system.
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.