In 2017, I gave a speech on puzzle complexity and provided the following clues for gauging the difficulty of a puzzle:
Suggested Level – If the puzzle is mass marketed, it probably comes with a suggested level of difficulty. In some cases, the level may be provided by the designer. After all, these designers are the world's greatest puzzle experts and have a lot of experience with puzzles and how well people can solve them. If you’re new to the puzzling world, you may find them underestimated. If you are an experienced puzzler, you may find them overestimated. Look for the ones with the icon of the guy pulling his hair out for the best puzzle experience. I know quite a few bald puzzlers.
|5 Piece Plate Burr|
Delight by Stéphane Chomine
Piece Variety – Usually puzzles where all the pieces are different are more difficult than when they are all the same. When they are all the same, you don’t have to worry about where each piece needs to go relative to the others. This could be a factor of N! for mathematicians.
Moves Required – In general, as the number of moves required to solve the puzzle increases, the complexity of the puzzle increases. However, some puzzles like N-ary puzzles may require very large numbers of moves to solve but may not necessarily be difficult.
|N-ary Puzzle - Spin Out by William Keister|
|Burr vs. Disentanglement|
Wookey Hole by Stewart Coffin
Rotations – For cubic dissections, the trend has been moving towards creating Turning Interlocking Cubes (TICs). I believe that Bernhard Schweitzer coined this phrase while doing a study on TICs. When solving a burr, knowing that a rotation is required is a significant clue. It activates all sorts of additional puzzle solving neurons in the brain while working on a puzzle. When you are completely stuck on solving a burr, you eventually ask whether a rotation is required. If the answer is yes, you happily go on searching for the rotation. If the answer is no, despair settles in. It’s as simple as that. Andrew Crowell is the current master of creating cubic dissection puzzles with rotations and they are all recommended.
NOS 5 Crenel by Gregory Benedetti
Number of Solutions – Many packing puzzles have multiple solutions. In general, it is expected that as the number of solutions increases, the chances of finding one becomes easier. For instance, the Soma Cube by Piet Hein has 240 ways to create a 3x3x3 cube and it is not that difficult to find one. The Half Hour puzzle by Stewart Coffin, however, has only one way to create a 3x3x3 cube and is much more difficult. I’m guessing that the Half Hour puzzle was named for how long it took Stewart to make the first copy of the puzzle given how much longer it took me to solve it.
|Two 3x3x3 Cubes - They Don't Look That Different!|
Soma by Piet Hein (Left) & Half Hour by Stewart Coffin (Right)
I’m much more careful now about giving out information on puzzle difficulty after an extremely embarrassing faux pas. While attending my first International Puzzle Party, hobnobbing with the cognoscenti of puzzledom, I put some of my puzzles out in the hotel lobby for others to play with. One attendee asked me if one of the puzzles was difficult to solve. It's easy I told him and then watched him struggle for hours trying to solve that puzzle. I think that he may have been shamed by my comment into trying to find the solution and instead of enjoying the puzzle, it may have become a burdensome task. Of course, I like to think that, like myself, he enjoys being frustrated. Why else would we do it!
If you are interested in the Man-O-War puzzle, you can find it at PuzzleMaster along with Hanayama Puzzles, the Soma Cube, and the Half Hour puzzle.