# 15 puzzle

The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle having 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. The goal of the puzzle is to place the tiles in numerical order. Named for the number of tiles in the frame, the 15 puzzle may also be called a 16 puzzle, alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle that has 8 tiles in a 3×3 frame. The n puzzle is a classical problem for modelling algorithms involving heuristics. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the taxicab distances between each block and its position in the goal configuration. Note that both are admissible. That is, they never overestimate the number of moves left, which ensures optimality for certain search algorithms such as A*. (Wikipedia).

The Fifteen Puzzle

Can you solve Sam Loyd's 14-15 puzzle?

From playlist My Maths Videos

Solution To The 15 Puzzler With A Twist

Here's the solution to the puzzle! First watch the puzzle video: https://www.youtube.com/watch?v=ts0-abh8Bi4 Then watch the solution: https://www.youtube.com/watch?v=w25x5AmHJBI As promised in the video, here's a link to a printable grid and pieces for the puzzle: http://goo.gl/fXdMw1 T

From playlist Math Puzzles, Riddles And Brain Teasers

15 + 4 puzzle

The 15 + 4 puzzle is a hinged version of the classic 15 Puzzle, with an extra 4 tiles. If you want to buy one of these, you will need the following two prints from Shapeways: Frame: http://shpws.me/SzQG Tiles: http://shpws.me/SzQH You will also need ten 8mm long M2 bolts and nuts to for

From playlist 3D printing

The Five Circle Puzzle

From playlist Tricks and Math Puzzles

18-Pieces Puzzle Wooden Toy 3D Model

Based on a Youtube video (https://www.youtube.com/watch?v=pulM5tHqZFg). There are seventeen identical pieces and one different, the locking. Modeled with Solidworks 2015. Rendered with Simlab Composer 6 Mechanical Edition. Free 3D model at https://skfb.ly/6ZDqQ.

From playlist Wooden Toys

Why the 14-15 puzzle is impossible, and how to solve it anyway

A bit of the math of the 15-puzzle, and some variants that shake up that math.

From playlist 3D printing

An Age Math Problem

From playlist Tricks and Math Puzzles

Arrange the Numbers Puzzle Solution

From playlist Tricks and Math Puzzles answers

Find the Five Numbers

From playlist Tricks and Math Puzzles

Solving Impossible Puzzles | Math Logic and Games

How can math help you find solutions to some of the world's trickiest puzzles? Watch as Art Benjamin uses logic to solve some classic games, including the 15 Puzzle, Box of Lights, and Peg Solitaire—all which have been driving people crazy for centuries. This video is episode eight from t

From playlist Math and Statistics

The World's Most Famous Puzzle Maker

*** STOP PRESS: BUY OUR BOOK WITH A SPECIAL DISCOUNT *** To celebrate achieving 500k subscribers, we're trying to say thank you in a couple of ways. We're able to offer our Cracking The Cryptic Greatest Hits book at a discount for a limited period. The coupon code is “500SUBS” and it can

From playlist Aad Van De Wetering Puzzles

Hyperbolic 29 puzzle

Buy from Shapeways: Hyperbolic 29 Puzzle Tiles: http://shpws.me/SJra Hyperbolic 29 Puzzle Frame: http://shpws.me/SJr9 Hyperbolic 12 Puzzle Tiles: http://shpws.me/SJrz Hyperbolic 12 Puzzle Frame: http://shpws.me/SJry Numbers to print (for either set of tiles): https://www.thingiverse.com

From playlist 3D printing

Your Chance To Finish A Puzzle By A Grandmaster

*** Today's Sudoku *** Today sees the return of one of the World's most brilliant setters, Qodec. And, although this puzzle is by no means easy, it isn't his hardest sudoku. Give it a try and see if you can finish a puzzle by a sudoku GM! You can play it at the link below: https://ap

From playlist Qodec Puzzles

Almost Out of GAS

Here are URLs for today's 5 GAS (Genuinely Approachable Sudoku) puzzles. Hat times are given as (two hats/one hat): GAS 456 – Count Different Sudoku by clover https://tinyurl.com/4evm67rh https://f-puzzles.com/?id=2hd43ctw (7:00/13:00) Normal sudoku rules apply. If a white circle appears

From playlist All the GAS - Genuinely Approachable Sudokus

The Fifteen Puzzle Part 2 + More Puzzles

The answer to Sam Loyd's 14-15 puzzle, and a few more fifteen puzzles to solve.

From playlist My Maths Videos

The 15 puzzle - solving the unsolvable 19th century Rubik's square

In this video the Mathologer has a close look at the granddaddy of all Rubik's "cubes", the puzzle that triggered the worldwide puzzle craze of 1880. Find out about how this puzzle managed to perplex millions of people, the mathematical Yin and Yang of permutations, and a set of false teet

From playlist Recent videos

Moves 2022 conference talk: Variants of the 15-puzzle and the effects of holonomy

A talk I gave at the 2022 Moves conference in New York City.

From playlist Talks

Helix cube puzzle

Prototype half frame: http://shpws.me/TiT4 One tile: http://shpws.me/TiT7 Full frame: http://shpws.me/TiT6 (will also require three 25mm long M2 bolts and three M2 nuts) 20 tiles: http://shpws.me/TiT5 Files for the half frame: https://www.printables.com/model/323666-helix-cube-puzzle-prot

From playlist 3D printing

Arrange the Numbers Puzzle

Use all the numbers once and only once. Enjoy! Next puzzle: http://www.youtube.com/watch?v=0QjmQlMJVgc Solution: http://www.youtube.com/watch?v=4-49PIdZQtM Previous puzzle: http://www.youtube.com/watch?v=mW3zTyXTwf4 Music by Bertrand Laurence http://www.bertrandlaurence.com used with permi

From playlist Tricks and Math Puzzles