Sequential Movement Puzzles: The History Of

Sequential Movement Puzzles

Combination puzzles, also known as sequential move puzzles, are a form of mechanical puzzle popularized in movies and culture. This category of puzzles represents two of the most famous puzzles of all time, the Rubik’s Cube and the Towers of Hanoi, as well as classic games like Solitaire.

This style of puzzle is solved by progressing from some initial state to a defined goal state by manipulating and moving the puzzle in different combinations. The puzzle is completed by achieving a particular combination, usually the grouping of colors, or creating an order. The object of the exercise is to complete them in as few moves as possible.

Classically, the quantity of moves available should be finite, usually very small – this distinguishes sequential from disassembly puzzles, where although there is a sequence of moves, they are typically not apparent. Also, the options available are constrained by previous moves – this distinguishes sequential move puzzles from assembly puzzles.

Gray Code Puzzles is a variety of puzzles which can be solved using some variation of Gray Code, a sequence of binary numbers in which any adjacent numbers are different in only one bit.



Here is a 3-bit Gray code in action:

0) 0 0 0

1) 0 0 1

3) 0 1 1  <-- change only the 2 bit

2) 0 1 0  <-- now change the 1 bit

6) 1 1 0

7) 1 1 1

5) 1 0 1

4) 1 0 0


The Towers of Hanoi and Chinese Rings work from this principle in order to find a solution. The Towers of Hanoi, from Planet of the Apes fame, where it is called the “Lucas Tower”, to study the intelligence of apes.

The Towers of Hanoi puzzle was invented by French mathematician Edouard Lucas, clever he marketed the product under the term N. Claus De Siam – an anagram of Lucas d’Amiens.

The classic version of the Towers puzzle comprises 3 pegs and a set of discs that graduated in size, a central hole cut into each piece allows you to transfer one peg to another. The object of the game is to move all the discs from the first peg to the third peg by moving only one disc at a time, and stacking the in their original order. The discs can only be moved to empty pegs OR pegs where the disc they are on is larger than their current disc – IE you can never put a large disc on a small disc.

The optimal number of moves required for solutions can be equated to 2n-1, when N is the number of discs.

The Tower of Hanoi puzzle follows some of the same logic as seen in river crossing riddles and measuring jug problems.

Sliding Puzzles

The classic Klotski puzzle or Hua Rong Dao is a prime example of a sliding puzzle that is categorized by sliding puzzle. Our Setting Sun Puzzle is a variation of the Klotski and is a favorite among our customers. This traditional Klotski rose to prominence in 1930's China. Based on a famous Chinese strategist, Cao Cao, a warrior from the Eastern Han Dynasty.

Legend has it Cao Cao was a master of evading capture through an arsenal of charm, street-smarts and cunning. You’ll need to use all the tools at your disposal to give your captors the slip.

Sliding block puzzles classically have ten pieces the Cao Cao piece is the main header; the remaining 9 pieces represent armed guards and other obstacles. It’s your job to manipulate these obstacles and get Cao Cao to freedom at the base of the board.

The minimum number of to complete the classic Klotski puzzle is 81 – although once again this is dependent on the number of pieces that are in the puzzle as there have been many adaptions and variations.


The classic Klotski puzzle has been transformed in to popular computer game, and was even featured in Windows 3.1 – in the Microsoft entertainment pack.

Twisty Puzzles

Undoubtedly the most popular of all the puzzle categories, these are puzzles for the 21st century. As the name indicates the solution my rotating a number of layers on a mathematical object – the movement is usually a based around and axis.

We can’t discuss sequential movement puzzles without at least touching on the Rubik’s cube, one of the few puzzles that have captured the imagination of a worldwide audience. Rubik’s cube are still remarkably popular among the hipster set and mathematical minds everywhere.  There are a ton of puzzle competitions for puzzlers or “cubers” everywhere: https://www.worldcubeassociation.org/results/competitions.php


Twisty puzzles are one of the most progressive puzzles styles, where the boundaries are constantly being pushed in design and manufacture. I’d recommend everyone check out the Pentaminx, which is a space-age behemoth if ever there was one. 12 Surfaces, 9 layers of dodecahedron infused madness.

Due to advancements in 3D printing, people are able to design and create their own puzzles.

Peg Solitaire and Jumping Puzzles

Peg solitaire is another form of sequential move puzzle – and another true classic in the genre. Peg solitaire is related to the Foxes and Geese – and is believed to be around 300 years old. The game is arranged with pegs in holes, typically the object is to jump over your pieces, either vertically, horizontally or diagonally. This process removes them from the board until you are left with a “single vacancy survivor” – which should be located in the same pot as the initial empty hole.

The “English” cross-shaped board is played on a 33-hole cross-shaped – the classic process for this solitaire style is to start with all the holes filled except the middle hole – patrons of Cracker Barrel may recognize this puzzle in its more familiar triangular format. A master solitaire puzzler will be able to complete a puzzle in as few moves as possible – the shortest solution to the English board is 18 moves.

In all there are 6 varieties of puzzle – the Continental Board, The German Board, the Asymmetrical Puzzle, Diamond 41 holes and Triangular – we feature many of these in our solitaire store.

August 09, 2015 by Sean Allan
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