Articles About Mechanical Puzzles

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Some of these articles about mechanical puzzles were published in back issues of Cleverwood’s Puzzling Times. We hope you find them interesting~



Sliding Block Puzzle Basics


Mechanical Puzzle Classification


The Difficulties With Difficulty Ratings


What Are Puzzles and Why Are They Puzzling?


What Makes a Great Puzzle?


How’d You Come Up With That?!


Perplexing Puzzlers


About Japanese Puzzle Boxes


Care of Japanese Puzzle Boxes


Advice for Puzzle Box Lovers Bound For Japan

The Difficulties With Difficulty Ratings

by Charlie Malcolmson, with contributions by Lionel Depeux, Nile Gardner, and Jerry Slocum
2001 by Charles J. Malcolmson - All Rights Reserved

There is no generally accepted system for rating the difficulty of mechanical puzzles. It’s not because no one has tried to devise a system. The main problem is that difficulty is subjective. You may feel that a particular puzzle is easy while someone else may think it’s very difficult.

Some of the factors that determine the difficulty of a puzzle for a particular person are:

bulletThe puzzle’s number of pieces
bulletThe puzzle’s number of moves
bulletThe puzzle’s number of unique (non-repetitive) moves
bulletThe puzzle’s complexity
bulletThe number of solutions possible
bulletThe puzzle’s similarity to other puzzles known to the solver
bulletMisleading tricks built into the puzzle, if any
bulletClues built into the puzzle, if any
bulletThe skills, knowledge, and abilities of the solver
bulletThe experience of the solver

It’s easiest to assign a reasonable difficulty rating to puzzles in the same family, or group. For example, a 12 move Japanese Puzzle Box is more difficult than a 4 move Japanese Puzzle Box. Here the relative difficulty is directly related to the number of moves required to open the box. But how difficult is the 4 move box? To a person who has never seen anything like it before, the 4 move box may be very difficult. To anyone who has ever opened any other Japanese Puzzle Box, the 4 move box is easy.

Difficulty ratings become more difficult to deal with when considering the relative difficulty of dissimilar puzzles. How difficult is a Juha 12 Cube compared to a 54 move Japanese Puzzle Box? Whatever difficulty rating we assign to a puzzle, someone can argue convincingly that the rating is wrong. Wrong for them, that is.

Lionel Depeux, a puzzle collector in France provides these insights into the difficulty question:

“Some puzzles are ‘intrinsically’ difficult, because they involve some sort of trick or because of their combinatorial nature involving so many possibilities that it would take anyone ages to try every possible combinations. The  ‘infinity’ puzzle or the Rubik’s cube or most packing puzzles are such puzzles, for instance.

As to most puzzles involving tricks, such as many boxes, I consider them as difficult because there is little logic in solving them. Sometimes, the solution is logical when it comes to the shape of the box, but this is not a rule, this is the designer’s will, and hence nobody may ever guess if there is logic or not in solving any such puzzle. That makes them difficult. Some people are  ‘gifted’ people and will guess the solution very quickly while others will get stuck until they eventually look at, or are being told, the actual solution.

The number of moves/steps required in order to solve a puzzle is not always accurate when it comes to evaluating the actual difficulty. For instance, Kamei’s  ‘Cubi 32’ box may be much more difficult than many  ‘n step’ secret boxes… but a classical 27 move Japanese secret box is always more difficult than a 12 move one.

I’d tend to consider that the difficulty rating should rather be given within a particular kind of puzzle. I have already solved a few complex puzzles (yes, this happens!…), and yet I still have one really nasty  ‘Bolt’n’nut’ puzzle that I could never solve, though it only comprises 4 pieces!

This is why I think you’re likely to fail if you’re trying to devise a sort of   ‘universal chart’ that may apply to any puzzle.

And Nile Gardner, another serious puzzle collector in California, USA adds this:

As you have noted each puzzle can be considered to have two difficulty ratings:

bulletRelative difficulty: The difficulty of the particular puzzle relative to others of its type. This can be indicated by a numerical or alphabetic rating.
bulletGeneral difficulty: The average amount of time required to solve the puzzle by a representative sample of people who try to solve the puzzle. This can be indicated in minutes, hours, days, years or millennia.

Serious puzzle collector will only pay attention to the relative difficulty knowing that the general difficulty measurement wouldn’t be a meaningful measurement relative to their ability. All others can use the combination of both measures to determine whether the puzzle will be too little or too much of a challenge.

Finally, mechanical puzzle expert and author Jerry Slocum, provides this insight:

"It seems to me that the dimension of difficulty is more related to the number of TYPES of moves, rather than just the number of moves. In many classical Japanese puzzle boxes, the same type of move is used every time. For these trick boxes adding additional moves adds very little or no additional difficulty in opening the box. But if the box includes different types of moves, such as moving a piece back rather than forward, or moving a piece only part way to the end of its path, it makes the trick box significantly more difficult.

In other words, if each move is a completely different type of trick, the solution is much more difficult than if the same basic move is repeated many times. For example trick locks usually use a sequence of tricks where each trick is completely different. These are much more difficult than the typical Japanese trick box where all the moves are essentially repeats of the same move."

So, as we can see, the question “How difficult is this puzzle” is not easily answered in many cases. Nevertheless, since a puzzle’s difficulty is a very important factor in the puzzles desirability, we must provide some indication of a puzzle’s difficulty. Here’s how we’re going to deal with puzzle difficulty ratings on the Cleverwood web site:

        One or more difficulty ratings will be used for each puzzle.

        If the puzzle is assigned a difficulty rating by the maker, we give the “Makers Difficulty Rating’ and rating system for that maker’s work. If we perceive the puzzle’s difficulty different than the maker’s rating we will explain why.

        We will assign a “Relative Difficulty Rating” where appropriate, as in the case of Japanese Puzzle Boxes. Groups of puzzles that have an objective difficulty factor that is directly correlated to the puzzle’s difficulty, like the number of moves, will be rated relative to each other. More moves usually, but not always, means greater difficulty.

        We will assign a “General Difficulty Rating” when appropriate, and will give the applicable criteria, that is, what makes it difficult – the number of combinations, for example. Puzzles that are not clearly part of a family or group, will be rated relative to the most similar puzzle of its type of which we are aware. For example, Eric Kelsic’s 13 move Repeating Puzzle Box is at least as difficult as a 54 Move Japanese Puzzle Box.

        Our ratings will be scaled for adults who like puzzles but do not consider themselves to be “serious” puzzle solvers. Serious puzzle solvers should adjust our difficulty ratings downward. “Very Difficult” becomes “Difficult” etc. People buying puzzles as gifts for people inexperienced with mechanical puzzles should adjust our difficulty ratings upward. “Easy” becomes “Moderate” etc.

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by Kathleen Malcolmson - 01/1997

Puzzles have existed throughout recorded human history in the form of riddles and other word puzzles. Mechanical puzzles are perhaps only hundreds of years old and are defined by world famous puzzle collector Jerry Slocum in his book Puzzles Old And New:

“A mechanical puzzle is a self-contained object, composed of one or more parts, which involves a problem for one person to solve by manipulation using logic, reasoning, insight, luck, and/or dexterity.”

Mechanical puzzles were first classified by Professor Hoffmann in his landmark book published in 1893 also titled Puzzles Old And New. Mr. Slocum expanded and modified Professor Hoffmann’s classifications into 10 main classifications as follows:

1. Put-Together Puzzles.
2. Take-Apart Puzzles|
3. Interlocking Solid Puzzles
4. Disentanglement Puzzles
5. Sequential Movement Puzzles
6. Puzzle Vessels
7. Dexterity Puzzles
8. Vanishing Puzzles
9. Impossible Object Puzzles
10. Folding Puzzles.

Some of these classifications are further divided into sub-classifications.

At Cleverwood, we are primarily interested in the first three types of puzzles. For example our magnetic Rhombus Puzzle is a put-together puzzle, Puzzle Boxes are take-apart puzzles, and Zig-Zags, Elephants, and Star Clusters are interlocking solid puzzles.

Mechanical puzzles are puzzling because they usually require one to think in unusual ways to solve them. They challenge our accepted perceptions of the world and how things work-our accepted, seldom examined assumptions are called into question. This explains why a child can often easily find the solution to a mechanical puzzle that eludes an adult.

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What Makes a Great Puzzle

by Kathleen Malcolmson - 01/1997

A great mechanical puzzle is one that is not only fun while attempting the solution, but before and after, as well. Before you solve it, it should be intriguing. You should be pulled into it with curiosity as to how it works. Touching it should invite you to open it or change it somehow. During the time that you’re trying to let the puzzle know who’s boss, you shouldn’t get too frustrated. Some puzzles are meant for ‘old hands’ while other puzzles just let you dip your toes in to see how you like it.

Everyone’s frustration level differs. You want enough frustration to challenge you but not so much that you are discouraged. Most people can do more than they think. A great puzzle will stretch what you think your limits are.

After you’ve finally solved it once, some puzzles may still take many more attempts to master. For example, a puzzle based on invisible magnetic attraction and repulsion will continue to be a challenge until you can develop a method that will minimize trial and error. Even after it is mastered it should still invite you to explore it more.

How was it made? How does it work? Does it look better on the desk or the coffee table? What kind of person could think up a thing like this?

It should delight you while you watch others try, in their own way, what you’ve already accomplished. By watching other people attempt to solve the same puzzle, you notice that there was more than one way to come to the same solution. Different people go about solutions in different ways. Watching others solve a puzzle you think you know well can provide new insights.

When choosing a puzzle for yourself or someone else, remember that a great puzzle will be fun before it is solved, while solving it, and after it has been solved.

Have fun!

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How’d You Come Up With That?! (and How You Can, Too!)

by Kathleen Malcolmson - 01/1998

The most common question that I get at craft shows is “How’d you come up with that idea?”. I’ll tell you how I come up with some of my ideas and how you can come up with some of your own.

First, I’ll tell you what I think a puzzle is. A puzzle is some-thing that makes you think. A puzzle doesn’t have to be made out of wood or plastic or cardboard or anything. Just trying to figure out how to divide twelve pieces of pizza among five friends is a puzzle. How to get your sister to let you borrow her tennis racket is a puzzle. How to get your homework done and watch The Simpsons on TV is a puzzle. You can make up some great puzzles with match sticks (or toothpicks).

Some puzzle ideas are simple, some complicated. The first puzzle I tried to make as an adult was a trick opening box. I wanted to have one, but couldn’t afford to buy one, so I thought it would be fun to figure out how to make one myself. It took me months! But I learned a lot about woodworking and puzzle making. Stuff I can use to make other puzzles!

I came up with another puzzle when I was working on something else. Frustrated and tired of cutting so many perfectly straight lines, I grabbed a piece of wood and cut a lot of squiggly lines in it from different sides of the wood and just sat down and played with it for awhile. That’s how my Zig-Zag puzzles got started.

Try out your ideas! It is very important to at least try. Some ideas won’t work out, but you’ll get more ideas while you’re working on the first one. Don’t be afraid of making mistakes. Some of the best lessons I have learned are from my mistakes. Even though I groan when I first discover that I have made a mistake, if I take time to think about it, I come up with an idea that fixes it, and sometimes even makes my project better than before! Use the talents you have, and develop new ones. Use the tools that you have, or make new ones. There’s so many different kinds of puzzles out there that you shouldn’t have to spend a lot of money to make your own. If you like mazes, all you need is a paper and pencil to start.

Designing and making puzzles is a puzzle itself. That must be why I like doing it. Most importantly, have fun. If you start to get frustrated, take a break. Sometimes great ideas will come to you when you’re doing something totally different. The brain is funny that way.

To help you get started on your own puzzle ideas, try out the library. They have lots of books about all kinds of puzzles, including jigsaws and crosswords. Some books even give you step by step directions on how to make some really great puzzles.

Now go get puzzled!

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Perplexing Puzzlers

by Kathleen Malcolmson - 01/1999

There are a lot of people out there who love solving puzzles (let’s call them puzzlers). There are just as many who couldn’t tell you, with any coherence, why they love solving puzzles. It’s just fun. There are many more people who think that those who have fun solving puzzles are weird (let’s call them non-puzzlers). Still, the non-puzzlers indulge the puzzle-solvers by providing them with more puzzles. The game seems to be, “Find one they can’t solve, that’ll fix ’em”! From my point of view, as a puzzler, this challenge only feeds the fire. As a result, friends and relatives are even more determined to find a puzzle to stump “the puzzler”. It’s a wonderful symbiosis, puzzlers provide entertainment for the non-puzzlers and vice versa.

Being a puzzler of the philosophical sort, there is one question that has perplexed me for quite some time that, I have recently found, interests other puzzle enthusiasts as well. The question being, “What do we all have in common that makes us enjoy puzzles so much?” If this query does not interest you, I bet this one will: when confronted by a friend, or significant other, who wants to spend some time solving a puzzle, the question in your mind, if not spoken, is “Why?”. Am I right? I consider both of these questions to be closely related.

In 1997, I had the opportunity to attend a gathering of puzzle enthusiasts, including historians, collectors and designers from all over the world. Besides all of us being extremely good looking, there appeared to be little, on the surface, that we had in common. I did note, with pleasure, that whenever there was a group of us together and someone would pull out a puzzle, everyone’s ears seemed to prick up and eyes begin to gleam as we would gather around in interest. When I pull a puzzle out in a “regular” group of friends, I can expect a mixture of mild curiosity, boredom and fear. Many puzzlers had an area of specialized interest such as sliding block puzzles, mechanical puzzles, packing problems, or secret opening boxes, but the mystery of the unknown sparked interest in us all.

One gentleman at the gathering noted that one common theme of interest to most of us is that we were “computer literate”. I like to romanticize a bit and consider that puzzlers are like the explorers of centuries gone by, mysteriously compelled to search for the unknown to fill in the gaps of the maps of the world (or mind) as we presently know it. Back to reality.

Recently, at an open jurying of fine woodworking, the jurors were commenting on my entry, an extremely convoluted-looking mahogany puzzle. The jurors were not aware which entrants made what entries. With a bewildering wave of glee and shock at their bluntness, I listened to them say that the person who designed this entry must have a demented brain! (The glee came from my puzzle designer’s slightly sadistic nature.) Even Merriam Webster’s Collegiate Dictionary, Tenth Edition, says under the “puzzle” entry, “... to baffle and disturb mentally...”. Now I can’t even argue with my friends when they call me mentally disturbed. At the opening reception of the exhibit at which my precious puzzle was on view, proudly displaying its name Metamorphic Puzzle, I overheard an onlooker comment, “They should call it Dementia. There’s that word again. If I didn’t find an answer to the question of what puzzlers have in common, at least I feel a little less “weird” knowing that there are others like me. Puzzler or non-puzzler, if you have any thoughts to share about what puzzlers have in common, please share them with me. I need all the hints I can get! And please, don’t use the “D” word.

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Advise for Puzzle Box Lovers Bound For Japan

by Kathleen Malcolmson - 02/2005

If you find yourself going to Japan and want to check out the puzzles, Tokyo and nearby Hakone are a good place to begin.

In Tokyo, almost any good toy store will have puzzles. Puzzles are much more popular in Japan than the US.

In the Akihabara (electronics) district of Tokyo there is a pushcart that is known for its selection of puzzles and its very friendly, helpful owner, Hirano-san. It is located in front of the Akihabara Department Store. He doesn’t speak much English, but that is not a problem. He is used to communicating and demonstrating to foreign visitors in puzzle-ese. Here is a link to a page that has directions and a photo of the cart and Hirano-san, so you’ll know what to look for. His hours can be unpredictable some days, so if the cart is closed, ask a neighboring cart if they know when he’ll be open. He usually opens at 10 A.M.

A couple other stores with good puzzle selections in Tokyo include, but are not limited to:
- Hakuhinkan Toy Park in the famous Ginza district. Via Train- JR Yamate-line, Shinbashi Station. 8-8-11 Ginza, Chuo-ku. Go directly to the top floor (4, I think). This is a big, fun place with lots of toys, videos, etc. Plan on spending some time. Non-puzzle note - Remember that DVDs need to be Region 1 for play on American/European machines. Japan is a different region. Video games also need a translator adaptor accessory (not language related). VHS tapes are playable in the US.
- Torito’s Puzzle Shop . Via Subway- Asakusa-line, Kuramae Station. 4-3 Kuramae 2, Taito-ku The web site will drive you nuts because it’s completely in Japanese with lots of photos of wonderful puzzles! If you can read Japanese, you’ll be fine. The shop is difficult to find but worth the adventure. It’s in a small space on the second floor of an office building. You should try calling just before you go to get directions. +81-3-5823-6873. English might be a problem, so you may need to find someone who can call and translate for you. Worth the trouble!

Hakone is a mountain resort at the foot of Mt. Fuji with a beautiful lake, named Lake Ashi (foot). Jerry Slocum, the puzzle collector and author has dubbed it “Puzzle Mountain” for good reason. Not much English is spoken here, but you can still make your way around because the people are very friendly and helpful. It is a long trip to travel just for one day, so you may consider staying overnight, like most visitors from Tokyo do. There are train schedules that make it relatively easy to travel without driving, and plentiful local buses and walkways once you arrive. Although many, many shops carry puzzles and puzzle boxes, two notable ones are Izumiya and Maruyama, both in Hakone Machi. Locals know these shops, so ask at a restaurant or bus stop. They both also have web sites. If you’re adventurous, just show up in Hakone Machi and take it from there, otherwise, you may want to do a little research and plan some sightseeing and outings. There is a lot more than puzzles in this area!

From Hakone, I highly recommend traveling by bus to the Yosegi Museum (Yosegi Kaikan) in Hatajuku. It is about a 20 minute ride from from Hakone-Yumoto station by bus. It is open every day from 9 to 5. There are also some wonderful puzzle box shops here, Hamamatsuya and Kanazashi. In my experience, no English is spoken here, but again, the people will do all they can to help you find your way. It is a small place on the bend of a mountain road and worth the time. You should walk around the town and perhaps find craftsman at their work and happy to show you what they are doing. Take credit cards.

I hope this information is a good start for you to make your own, personal puzzle adventure in Japan.

Just one more thing, there are many sites and places that puzzle people find interesting in Tokyo, like the Science and Industry Museum, or Tokyo Tower’s Trick Art Museum. Tell people who live there your interests and ask for suggestions on places to visit. I’m sure there are hundreds of places I don’t know about that you may discover on your own. Have a great, puzzling adventure in Japan!


A mechanical puzzle is a self-contained object, composed of one or more parts, which involves a problem for one person to solve by manipulation using logic, reasoning, insight, luck, and/or dexterity.” - Jerry Slocum

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