Folding Puzzles(Part 1)
by Pantazis Constantine Houlis
The author always felt that the folding mechanism based on the Rubik's Magic is brilliant, and despite the great marketing of the past, not much justice had still been done to show its proper potential to the world. It was the main reason the author have made dozens of mechanically different designs, as well as adaptation of a variety of mathematically efficient themes. The general family of puzzles are defined as FP (folding plate). In the past, all commercial square FP puzzles used a number of tiles which was a multiple of four. After searching a bit, I found out that a few square FP puzzle experts have created slightly different designs. Juozas Granskas had done different types with six, seven (by "bandaging" two 4-tile FP puzzles), and ten tiles. Adam Cowan did FP puzzles with six and ten tiles, and Tim Browne created a mini 6-tile FP puzzle. It is essential to divide those FP puzzles into three categories: 1. Closed Loop FP
puzzles, such that each tile is connected to exactly two neighbour tiles,
Based on the author's personal experience, a difficulty "Level" number (using a 1-10 scale - 10 is the hardest) is shown. For the Square Tile Closed Loop FP puzzle mechanism (which is found in the majority of the FP puzzles) the notation M(x,y,z) is used as defined in the FP puzzle classification article [Pantazis Constantine Houlis, A classification of Folding Plate Puzzles, CFF 78, March 2009, pp. 4-9]. The first letter "M" of the notation was derived from the word "Myth", denoting their rare nature (it can also be assumed to be the word "Magic"). All of those puzzles are hardly available today, as only a limited number (or none at all) of copies had been made. This article documents this effort as it is certain that in the future it will inspire more new findings.
1. Build the Color Bench.
Level: 5. Type: M(8,0,0).
Figure 2: Unsolved and solved states of the Build the Bench Puzzle, and the color configuration which is being used.
The Bronze Olympic Challenge is a Bandaged Loop FP puzzle made of two four-square-tile Closed Loop FP puzzles which share one tile (so in total it has seven tiles). The bandaging creates an extra challenge for the puzzle solver. Juozas Granskas was the first to make the mechanism found in this puzzle, by using a different theme [4]. The Silver Olympic Challenge is also a Bandaged Loop FP puzzle. This time it is made of two six-square-tile Closed Loop FP puzzles which share three tiles (so in total it has nine tiles). Since the number of shared tiles is high, solving can sometimes lead to dead ends. It is one of the trickiest FP puzzles ever made. The Golden Olympic Challenge is a Closed Loop FP puzzle made of ten tiles. Its freedom of movement (compared to the Bronze and Silver Olympic Challenges) makes solving more difficult, as the choices are much more and the solution is unique.
This Secret Cube Move sequence (which needs extra care when performed) starts from the flat state and ends to the cubic state. Depending on the starting point (as there are many flat states), the cubic state result can be manipulated accordingly. When going from "flat to cubic" state or from "cubic to flat" state, the FP puzzle will automatically snap without any bad effects. But like all FP puzzles, after performing a tight move, it is good to check all strings are in place. In general, the Magic Dino Cube is actually two cubes (which means that the puzzle has two cubic solutions), one of which represents the four colored Dino Cube (front side when flat), and the other represents the six colored Dino Cube with the dinosaur pictures (back side). In the back side, four colored lines have been added on each side of the square, to denote the color of the tile that is supposed to be adjacent to the other when solved. This proves the importance on detail which is combined with providing a unique solution for both sides.
"After the enigma of the Sphinx was solved, the Gods were furious as their best puzzle was revealed to mortals. Thousands years later, and after thinking carefully of how to punish the ever curious humans, they sent to them a small magic puzzle, which was made of seven tiles that symbolised that the magic box was more powerful than all the seven wonders of the ancient world put together". This puzzle is more flamboyant version of the Pantazis'
Box using the properties of the transparent tiles. Here, accurate tools
were used to nicely cut the glittery paper inserts such that after the
box shape is formed, we can see through as many as three tiles in a row.
There are four types of punched cuts, each of which represents summer
(sun), autumn (leaf), winter (snowflake), and spring (flower). Special
calculations were made to ensure the existence of exactly two solutions.
The goal of the puzzle is simple. When irritated, the octopus becomes red and prepares to use their ink to escape. The puzzle solver is required to "calm down" the octopus by unscrambling the blue color (which will scramble the red color).
Figure 9: The Magic Ultimaze Puzzle.
The Magic Ultimaze has two different patterns in it. It has continuous diagonal lines, and also, horizontal and/or vertical lines made of colorful marbles. Each type of lines has two solutions, a flat solution with a closed loop line (around both sides of the flat state), as well as a cubic solution with a closed loop line. There is also a fifth solution made of two separated closed loops. Note that in all the above mentioned solutions there are no open loop lines. All solved closed loops pass through all the tiles at all times.
As a puzzle, it has way too many restrictions because of its too many combined loops. This means that movement of this 30-tile FP puzzle is a tiny fraction of the ones that exist in other puzzles. And although it can still be very playable, because of the impressive size ration between contracting and extending, it may be best regarded as a special decorative design rather than a puzzle.
So now, to break another boundary, we may imagine
a FP puzzle which only has one side, that is, it is connected in the same
way as a Möbius Strip [1].
A bit of theoretical view is needed here. The normal 8-tile Rubik's Magic, as well the 8-tile "Frame" puzzle (e.g. Flexible Tetragon) are different in that one tile is connected differently by "half turn" [3]. That creates a parity difference between the two puzzles making them mechanically different. But what if, only one side of the tile was connected differently? Then we would have "half parity" or in other words a half-turn which is the way a Möbius Strip is made in FP puzzles. While stringing the tiles for this type of puzzles, the trickiest part is obviously the last step. It is the step where you must make the half turn twist to give the puzzle the Möbius Strip form. But after understanding how the last part should be connected (to close the loop) and by moving two tiles on the other side (which does not affect the final form of the puzzle), the final stringing can be easily done without any stretching whatsoever. In other words, if we have a magic puzzle in a Möbius Strip form, the stringing of the puzzle allows slightly folded flat shapes to be formed too, so stringing it in that state is easy. Now, seeing the shape of a Möbius Strip on an 8-tile FP puzzle (with big angles between very few tiles) is not the easiest task, but we can certainly do so on FP puzzles with more tiles (and the more the tiles, the smaller the angles between the tiles to reach the Möbius Strip form). The "Magic Line" as seen in the image above, is an 8-tile FP puzzle, which uses Mr Escher's ant theme. The goal of the puzzle is change the position of the ants.
The theme of this 21-tile Closed Loop FP puzzle is based on the Chinese game Mahjong. It is played like a mix between a domino and a card game, and it is played with 144 different block tiles, out which 42 are unique.
The second solution (photos below) looks more like the style when four players have spread their Mahjong pieces on the table. It is a very elegant and carefully made puzzle. And because of its natural creme color (similar to the original Mahjong pieces), it looks as if it was made of ivory.
TO BE CONTINUED TO PART 2 (to be made soon) |
To view a better analysis of some of those
(and other!) puzzles, click
here
To view some videos of those puzzles, click
here
To view more FP photos please click
here
To contact Pantazis, send an email to
All designs are copyrighted, while some are patented.
Pantazis Constantine Houlis 1998-2013