The 15 Puzzle

Short Video Series (SVS-0022)
The 15 Puzzle

📫𝐎𝐮𝐫 𝐅𝐁 𝐏𝐚𝐠𝐞:
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📚𝐃𝐚𝐯𝐢𝐝'𝐬 𝐁𝐨𝐨𝐤𝐬
📕 𝗪𝗲𝗶𝗿𝗱 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝗜𝗻𝗳𝗶𝗻𝗶𝘁𝘆 𝗮𝗻𝗱 𝗕𝗲𝘆𝗼𝗻𝗱
(https://www.amazon.com/Weird-Maths-Ag...)
📙 𝗪𝗲𝗶𝗿𝗱𝗲𝗿 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗘𝗱𝗴𝗲 𝗼𝗳 𝘁𝗵𝗲 𝗣𝗼𝘀𝘀𝗶𝗯𝗹𝗲
(https://www.amazon.com/Weirder-Maths-...)
📗 𝗪𝗲𝗶𝗿𝗱𝗲𝘀𝘁 𝗠𝗮𝘁𝗵𝘀: 𝗔𝘁 𝘁𝗵𝗲 𝗙𝗿𝗼𝗻𝘁𝗶𝗲𝗿𝘀 𝗼𝗳 𝗥𝗲𝗮𝘀𝗼𝗻
(https://www.amazon.com/Weirdest-Maths...)
** The kindle versions are available
*** For more details : http://weirdmaths.com/

📄𝗧𝗿𝗮𝗻𝘀𝗰𝗿𝗶𝗽𝘁𝗶𝗼𝗻:
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 – 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. There’s 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 you’re wasting your time!

#fifteen #puzzle #15