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The 15 Puzzle

ะะพะบะฐะทะฐัั ะพะฟะธัะฐะฝะธะต
Short Video Series (SVS-0022)
The 15 Puzzle
๐ซ๐๐ฎ๐ซ ๐ ๐ ๐๐๐ ๐:
๐๐๐๐ฏ๐ข๐'๐ฌ ๐๐จ๐จ๐ค๐ฌ
๐ ๐ช๐ฒ๐ถ๐ฟ๐ฑ ๐ ๐ฎ๐๐ต๐: ๐๐ ๐๐ต๐ฒ ๐๐ฑ๐ด๐ฒ ๐ผ๐ณ ๐๐ป๐ณ๐ถ๐ป๐ถ๐๐ ๐ฎ๐ป๐ฑ ๐๐ฒ๐๐ผ๐ป๐ฑ
๐ ๐ช๐ฒ๐ถ๐ฟ๐ฑ๐ฒ๐ฟ ๐ ๐ฎ๐๐ต๐: ๐๐ ๐๐ต๐ฒ ๐๐ฑ๐ด๐ฒ ๐ผ๐ณ ๐๐ต๐ฒ ๐ฃ๐ผ๐๐๐ถ๐ฏ๐น๐ฒ
๐ ๐ช๐ฒ๐ถ๐ฟ๐ฑ๐ฒ๐๐ ๐ ๐ฎ๐๐ต๐: ๐๐ ๐๐ต๐ฒ ๐๐ฟ๐ผ๐ป๐๐ถ๐ฒ๐ฟ๐ ๐ผ๐ณ ๐ฅ๐ฒ๐ฎ๐๐ผ๐ป
** The kindle versions are available
๐๐ง๐ฟ๐ฎ๐ป๐๐ฐ๐ฟ๐ถ๐ฝ๐๐ถ๐ผ๐ป:
The Fifteen Puzzle is a sliding-tile puzzle, which the American Sam Loyd claimed to have invented in the 1870s but that in fact was invented by Noyes Chapman, the Postmaster of Canastota, New York. It became a worldwide obsession, much as Rubik's cube did a century later.
Fifteen little tiles, numbered 1 to 15, are placed in a four by four frame in serial order except for tiles 14 and 15, which were swapped around. The lower right-hand square is left empty. The object of the puzzle is to get all the tiles in the correct order. The only allowed moves are sliding counters into the empty square.
Everyone it seemed was caught up with the craze โ playing the game in horse-drawn trams, during their lunch breaks, or when they were supposed to be working. The game even made its way into the solemn halls of the German parliament.
Loyd offered a $1,000 reward for the first correct solution. But, although many claimed it, none were able to reproduce a winning series of moves under close scrutiny. Thereโs a simple reason for this, which is also the reason that Loyd was unable to obtain a US patent for his invention.
According to regulations, Loyd had to submit a working model so that a prototype batch could be manufactured from it. Having shown the game to a patent official, he was asked if it were solvable. "No," he replied. "It's mathematically impossible." Upon which the official reasoned there could be no working model and therefore no patent!
Given a random arrangement of tiles, can we know in advance if we have one of the unsolvable kind? Very easily. Simply count how many instances there are of a tile numbered n appearing after the tile numbered n + 1. If there are an even number of such inversions, the puzzle is solvable, otherwise youโre wasting your time!
#fifteen #puzzle #15
The 15 Puzzle
๐ซ๐๐ฎ๐ซ ๐ ๐ ๐๐๐ ๐:
๐๐๐๐ฏ๐ข๐'๐ฌ ๐๐จ๐จ๐ค๐ฌ
๐ ๐ช๐ฒ๐ถ๐ฟ๐ฑ ๐ ๐ฎ๐๐ต๐: ๐๐ ๐๐ต๐ฒ ๐๐ฑ๐ด๐ฒ ๐ผ๐ณ ๐๐ป๐ณ๐ถ๐ป๐ถ๐๐ ๐ฎ๐ป๐ฑ ๐๐ฒ๐๐ผ๐ป๐ฑ
๐ ๐ช๐ฒ๐ถ๐ฟ๐ฑ๐ฒ๐ฟ ๐ ๐ฎ๐๐ต๐: ๐๐ ๐๐ต๐ฒ ๐๐ฑ๐ด๐ฒ ๐ผ๐ณ ๐๐ต๐ฒ ๐ฃ๐ผ๐๐๐ถ๐ฏ๐น๐ฒ
๐ ๐ช๐ฒ๐ถ๐ฟ๐ฑ๐ฒ๐๐ ๐ ๐ฎ๐๐ต๐: ๐๐ ๐๐ต๐ฒ ๐๐ฟ๐ผ๐ป๐๐ถ๐ฒ๐ฟ๐ ๐ผ๐ณ ๐ฅ๐ฒ๐ฎ๐๐ผ๐ป
** The kindle versions are available
๐๐ง๐ฟ๐ฎ๐ป๐๐ฐ๐ฟ๐ถ๐ฝ๐๐ถ๐ผ๐ป:
The Fifteen Puzzle is a sliding-tile puzzle, which the American Sam Loyd claimed to have invented in the 1870s but that in fact was invented by Noyes Chapman, the Postmaster of Canastota, New York. It became a worldwide obsession, much as Rubik's cube did a century later.
Fifteen little tiles, numbered 1 to 15, are placed in a four by four frame in serial order except for tiles 14 and 15, which were swapped around. The lower right-hand square is left empty. The object of the puzzle is to get all the tiles in the correct order. The only allowed moves are sliding counters into the empty square.
Everyone it seemed was caught up with the craze โ playing the game in horse-drawn trams, during their lunch breaks, or when they were supposed to be working. The game even made its way into the solemn halls of the German parliament.
Loyd offered a $1,000 reward for the first correct solution. But, although many claimed it, none were able to reproduce a winning series of moves under close scrutiny. Thereโs a simple reason for this, which is also the reason that Loyd was unable to obtain a US patent for his invention.
According to regulations, Loyd had to submit a working model so that a prototype batch could be manufactured from it. Having shown the game to a patent official, he was asked if it were solvable. "No," he replied. "It's mathematically impossible." Upon which the official reasoned there could be no working model and therefore no patent!
Given a random arrangement of tiles, can we know in advance if we have one of the unsolvable kind? Very easily. Simply count how many instances there are of a tile numbered n appearing after the tile numbered n + 1. If there are an even number of such inversions, the puzzle is solvable, otherwise youโre wasting your time!
#fifteen #puzzle #15
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