The first group of puzzle may seem like a collection of completely different puzzles at first, and it includes a Japanese Karakuri box, a big burr from Australia, several metal puzzles, some elephants, little cube boxes, and several sliding puzzles, and then there is the big one with a good colleciton of switches. So what's the common properties of these all (and even more not in my rollection)?
All of them have properties qualifying them as "n-ary puzzles".
It started with the old Chinese Rings puzzle and the discovery that the rings can be interpreted as bits (0 or 1) and then the puzzle and its solution would resemble the Gray Code, which originates in coding theory. Later on, ternary puzzles (like the Crazy Elephant Dance) were designed lifting the puzzles from binary to ternary, with all pieces having three states (0, 1, or 2). More and more puzzles came and were determined to be n-ary, with the record holder so far being the 15-ary "Generation Lock". Read more in this very mathematical analysis here.
Starting with the original Kugellager I collected some information on n-ary puzzles and integrated them into my article about the Kugellager. It contains some information on puzzles I do not have and you can download it here: Kugellager.pdf. Enjoy reading!
.JPG "Zankeisen mini")
.JPG "Metal Chinese Rings")
.JPG "Chinese Rings 9")
.JPG "Vintage Chinese Rings")
.JPG "computer loops")
.JPG "SpinOut")
.JPG "SPIN-OUT")
.JPG "The Brain")
.JPG "Small Cubi")
.JPG "Hexadecimal Puzzle")
.JPG "Bin Laden")
.JPG "Frame+Loop Trio")
.JPG "Frame+Loop Quartet")
.JPG "Frame+Loop Quintet")
.JPG "Frame+Loop Sextet")
.JPG "Rudenko Disk")
.JPG "Rings Disentanglement")
.JPG "Fidgety Rabbits binary")
.JPG "Left-Right Chinese Rings")
.JPG "Eureka 3D Puzzle H")
.JPG "Binary Key II")
.JPG "Ferris Wheel")
.JPG "Hexadecimal Puzzle 2013")
.JPG "Expansion V")
.JPG "Binary Burr")
.JPG "Dispersed GC Lock")
.JPG "Quatro")
.JPG "Steuerrad")
.JPG "Labnary")
.JPG "Binary Bud")
.JPG "Frame+Loop Octet")
.JPG "Bicomplementary formation b/b:1/2")
.JPG "Rat Race")
.JPG "Tree Puzzle")
.JPG "New Puzzle Rings 3")
.JPG "New Puzzle Rings 5")
.JPG "Pin Burr 2")
.JPG "Frame+Loop Septet")
.JPG "Alle Schiebung")
.JPG "Wicked Wire Fish")
.JPG "The Brain")
.JPG "Barcode Burr (printed)")
.JPG "Computer Puzzler No 2")
.JPG "Computer Puzzler No 5")
.JPG "Trapeze variant")
.JPG "Unknown Disentanglement 2")
.JPG "DITWIBIN")
.JPG "Tricky Frame")
.JPG "Tricky Mouse")
.JPG "Drunter und Drueber")
.JPG "Fibula Puzzle")
.JPG "Bin Laden Too")
.JPG "Elephant SpinOut")
.JPG "Elephant Wire Puzzle")
.JPG "Delirium 13")
.JPG "Binary Burr 3 small")
.JPG "Binary Burr 4 small")
.JPG "Binary Burr 5 small")
.JPG "Binary Burr 6 small")
.JPG "Binary Burr 7 small")
.JPG "Binary Burr 8 small")
.JPG "Binary Burr 9 small")
.JPG "Binary Burr 10 small")
.JPG "Digits' Compressor")
.JPG "B-Box, Reactor")
.JPG "Dingo Trap")
.JPG "Airplane")
.JPG "Mechanic Cubi")
.JPG "JUNC")
.JPG "Binary Ladder Disentanglement*")
.JPG "Mountain Trail")
.JPG "Alken/Kenal")
.JPG "Corn on the Cob I")
.JPG "Corn on the Cob II")
.JPG "Corn on the Cob III")
.JPG "The Key Puzzle")
.JPG "Bald Eagle")
.JPG "Buggin")
.JPG "xBrain binary")
.JPG "New Secret Box IV")
.JPG "Electro 2")
.JPG "Reverse Chinese Rings")
.JPG "Second-order Chinese Rings")
.JPG "Third-order Chinese Rings")
.JPG "Disordered Chinese Rings")
.JPG "Mountain Trail II")
.JPG "Double Image")
.JPG "Loopary Branch")
.JPG "Barcode Burr (printed)")
.JPG "Crossing")
.JPG "SpinOut mini")
.JPG "Barcode Burr Master Set Upgrade")
.JPG "Chinese Soft Ring")
.JPG "Corn on the Cob IV")
.JPG "Corn on the Cob V")
.JPG "Corn on the Cob VI")
.JPG "Catacombs")
.JPG "Chinese Soft Ring")
.JPG "Piano")
.JPG "Rainbow")
.JPG "4L Bin")
.JPG "Seahorse")
.JPG "Faraday Cage")
.JPG "Panex Junior")
.JPG "5L Bin")
.JPG "YPANEX")
.JPG "Railings")
.JPG "Binary Disk")
.JPG "Ratchet")
.JPG "Sensi Box")
.JPG "B-Bar")
.JPG "Crazy Elephant Dance")
.JPG "Tern Key")
.JPG "Ternary Burr")
.JPG "K323")
.JPG "Auf dem Holzweg")
.JPG "Rudenko Clips")
.JPG "Sliding-block Chinese-Ring-Style Puzzle")
.JPG "Fidgety Rabbits ternary")
.JPG "Matroshka Rudenko")
.JPG "Gordian Knot 2")
.JPG "Gordian Knot 4")
.JPG "Gordian Knot 6")
.JPG "Gordian Knot")
.JPG "Japanese disentanglement")
.JPG "Towers of Hanoi")
.JPG "Lego Ternary Gray Code Puzzle")
.JPG "Spiralschloss")
.JPG "Uhrwerk")
.JPG "N522")
.JPG "GC machine ternary")
.JPG "Railing with Draining ternary")
.JPG "Electro 1")
.JPG "Little Gordians Knot")
.JPG "Six Bottles")
.JPG "Viking Box")
.JPG "Complementary P-arity")
.JPG "Num Lock")
.JPG "Panex Squared")
.JPG "Find my Hole")
.JPG "Lock 14")
.JPG "N5")
.JPG "N52")
.JPG "N522222222")
.JPG "Bi-Nary")
.JPG "Double Loop")
.JPG "Uhrwerk")
.JPG "Bi-Nary")
.JPG "Racktangle")
.JPG "MixTer-MaxTer")
.JPG "Panex Gold")
.JPG "Disc + Crown CFF 100 Jubilee Edition Puzzle")
.JPG "Fishing Hook Chain 9-Ring")
.JPG "B-Nary")
.JPG "Super-CUBI (small)")
.JPG "Aquarius Drawer")
.JPG "The Bell")
.JPG "xBrain ternary")
.JPG "Planex")
.JPG "Jack-in-the-Box")
.JPG "Steuerrad-Kiste*")
.JPG "Sluice and Ships 6:5/N12")
.JPG "Six Keys Box")
.JPG "Aquarius Box (small)")
.JPG "5 times 5 times 5")
.JPG "A Slide-Ly Tricky Tower")
.JPG "Crazy Elephant Dance")
.JPG "Ternary Pin Burr")
.JPG "Stacker")
.JPG "N-Airy Box")
.JPG "ReTern Key with Circular Pieces (Coin Release)")
.JPG "The Tippenary Mystery Tour")
.JPG "N3 Box")
.JPG "Coherent Convoys")
.JPG "Telefon Box")
.JPG "Magestic 3")
.JPG "Eurofalle 8 / Auf dem Holzweg")
.JPG "Stern Box")
.JPG "Shuttle Run")
.JPG "Shoulder To Shoulder")
.JPG "K419")
.JPG "MMMDXLVI")
.JPG "Reflection")
.JPG "No Full Pirouette!")
.JPG "xBrain quaternary")
.JPG "Sequence Cube")
.JPG "Digi Fork-Lock")
.JPG "Gear Box")
.JPG "Panex Galaxy")
.JPG "Square Hanoi")
.JPG "Switched Maze")
.JPG "Egyptian Coin Trade")
.JPG "MiBinity I")
.JPG "Ziggurat")
.JPG "Zigguflat")
.JPG "Zigguflat (4 pieces)")
.JPG "Zigguflat (8 pieces)")
.JPG "Ziggutwist")
.JPG "Zigguchain")
.JPG "Zigguchain 12 links")
.JPG "Kugellager")
.JPG "Kugellager 8")
.JPG "Die Welle")
.JPG "Sliding Lock Puzzle")
.JPG "Mysterians")
.JPG "Frequency Doubler 1")
.JPG "Frequency Doubler 2")
.JPG "Cross + Crown 2013")
.JPG "Power Tower (mix base - var st)")
.JPG "Quadrupled Quadlooplet")
.JPG "Voidlock Metal")
.JPG "Visible 5-Ary Drawer (Quinary)")
.JPG "Ternary / Quinary Cube")
.JPG "Vertical")
.JPG "White Bow-Tie")
.JPG "Void Box")
.JPG "Lager Lock")
.JPG "Tvnary")
.JPG "Lock 250+")
.JPG "Cast Infinity")
.JPG "Merry-go-round")
.JPG "Slidebox")
.JPG "Salva")
.JPG "Kugellager 7")
.JPG "Cross + Crown 7")
.JPG "MiSenary Puzzlebox")
.JPG "Entwined Loops Lattice")
.JPG "Septenary Cube")
.JPG "Devil")
.JPG "Num Lock (mixed base)")
.JPG "Black Bow-Tie")
.JPG "O.M.G")
.JPG "Jellyfish")
.JPG "Jack's Ladder")
.JPG "Seestern")
.JPG "Generation Lock")