The Assembly or Put-Together class includes those puzzles which entail the arrangement of pieces to make specific shapes. For the most part, the order in which the pieces are put together does not matter. The puzzle may include a container or tray. If the pieces interlock, the puzzle belongs in the Interlocking class.

Here are my groupings:

Simply stated, the challenge of a packing puzzle is to fit a given set of pieces into a container. The boundaries are either enforced by walls and a lid, or sometimes just walls, with the "lid" implied by the requirement that no piece extends beyond the level of the walls. The container might also be more of a tray, especially if the pieces don't stack in 3 dimensions.

Now, if you consider this task in the abstract, the entire container could be construed as implied rather than physical, and then many assembly puzzles could be considered to be packing puzzles. For example, the SOMA cube could be re-cast as "fit the pieces into a cubic box." In addition, you can shoehorn dissections in here by thinking of the original form as the "container" - the objective is to re-construct the original form, which is tantamount to fitting the pieces back into this abstract container.

For my purposes here, I will include a puzzle in the "packing" category if there is a physical container, and some pieces to cram into it. In rare instances the container is similar to the pieces themselves. Sometimes the puzzle is presented with a subset of all the pieces except for one of them packed into the container, with seemingly no room for the additional piece, and the objective being to rearrange the pieces to make the last piece fit, too.

Take a look at Erich Friedman's Packing Center.

Bill Cutler has written an interesting essay on box packing puzzles.

Hercules - B&P Nice quality and poses just the right amount of challenge.	Crazy L A very nice little packing challenge, from the Puzzle and Craft Factory.	Four T's - Binary Arts/Thinkfun	Houses and Factories Designed by Richard Hess - distributed by B & P
Lucky 7 - Melissa & Doug	Blockade - B&P Blockade is like Lucky 7 - both use 3 small and 4 large L shaped pieces, but Blockade also has pins on the board and corresponding holes in the pieces. Lucky 7 is trivial to solve - Blockade adds a little (but not much) challenge.	Butterfly - Nature's Spaces Fit nine identical penta-hexes into a triangular frame. Only one arrangement will work.	Frog Pond - Nature's Spaces Fit nine identical tetra-hexes into a triangular frame.
Snake Pool Eleven cubes are loosely strung along an elastic to form a cube snake. Fit the snake flat in the tray - the "pool." There are at least four different solutions. The cubes are 3/4", the tray opening is 3.25" square. The snake configuration is: 3+2+2+2+1+1 (where a + denotes a right-angled bend that can swivel). Erich Friedman shows various square-in-square packings on his Packing Center site, but I don't think the solution shown for 11 squares works with this particular cube snake configuration.		Packing Quarters - B&P	Kinato Kinato is a very nicely packaged puzzle from Ravensburger. Sixteen triangles are threaded via clever swivel connections. Arrange them into a large triangle with the proper pattern. I found it at jigsawjungle.com.
The following tray-packing puzzles were all designed by Edi Nagata. Edi sells versions in 2-sided trays, made from MDF. A couple were offered by Bits and Pieces with wooden 2-sided trays and aluminum pieces, other single-sided versions in CD cases by Embrain via Torito.
Pencil Case	Arrow Case aka Packing Arrows - B&P	Shirt Case Purchase the 2-sided MDF version from Edi, or the single-sided CD-case versions "Shikoku" and "Australia" from Torito.
Cat Case aka Cats in a Cradle - B&P	Cup Case	Baby Ducks Case

This is a special group where the pieces aren't identical, but they are related by some rule or theme, which distinguishes them from those puzzles in the more generic group having an assortment of dissimilar pieces. Some of the puzzles in the latter group may languish there though they belong in this section because I am unaware of the rule relating the pieces...

Nine Squared - Tom Lensch All nine pieces have identical thickness but each has a different combination of length and width selected from discrete increments within a narrow range. When arranged correctly into the tray they simply drop in and out with no binding. Several incorrect packings seem like they should fit, if only you press down a little... wrong!

Apothecary's Cabinet - Constantin (purchased at GPP) Each "drawer" has a combination of side tabs and portions of the row separators, and is equivalent to a rectangle with each side having either a tab or a notch. There are 2^4=16 possible arrangements including rotations and reflections. The knobs on the drawers require the reflections. The fact that the side tabs/notches are off-center requires the rotations. This puzzle is a nice realization of a 4x4 heads/tails edgematching puzzle, but includes a cabinet/tray/frame which constrains the solution, since it has all notches along the left and top, and all tabs along the right and bottom. If you assign a 4-bit binary ID to each drawer using 0 for a notch and 1 for a tab, the low bit for the top and high for the left side, then one solution is: 15 7 5 9 14 4 8 13 10 6 1 12 11 2 3 0 For issues 61 and 62 (Nov 2003) of the CFF newsletter, Dieter Gebhardt wrote articles analyzing this puzzle, and in issue 62 reports results derived by Jacques Haubrich.

Digits - Constantin Fit the 10 digits into the tray.

Partridge Puzzle by Robert Wainwright obtained from Robert at the 2007 NYPP Kadon offers some of Erich Friedman's "Partridge" puzzles. In an "anti-Partridge" puzzle, there is one largest piece, and the count goes up as the pieces shrink.

Karin's Star Cluster An entry in the IPP24 Design Competition.	Tessellating Galaxies - JVK	Sun Dance - JVK	The City 2001 Binary Arts (Thinkfun) Pack six heptominoes (3 distinct pieces and their mirror images) in the 6x7 tray. Nice metal pieces with 3D abstract buildings on them which prevent the pieces from being flipped and exclude most of the otherwise possible 80 assemblies.
Geometrex Set - Ormazd, Nabucho, and Quirinus In each case the pieces can be rearranged within the tray to fit in an extra square.	Fit To A Tee - Thinkfun A nice metal tray-packing puzzle from Thinkfun. Pack the 9 pieces representing golf holes complete with tees, sand traps, and pins, into the base. The base presents a challenge on each side (the front and back nines), with different arrangements of fixed water hazards to work around. Oh, and just as on a real course, abut each flag with the tee of the next hole!	Fantastic Island	The "845 Combinations" puzzle is almost like pentominos... here is a solution to the 845 puzzle.
Adam's Cube	One Way	Boxed In - Milton Bradley	Circle Challenge - Melissa & Doug A good one for kids - work on it from the inside out. The pictures on the pieces are merely decorative.
Magic Block (MCS promo)	Figa Block	IQ Block	Double Cross - Mag Nif There are four pink plastic pieces and the tray. The objective is to form a cross (plus sign) in the tray.
Sleazier - Pavel Curtis based on Stewart Coffin's Four Sleazy Pieces (#169A) Fit the 4 polyominoes into the tray. IPP25	Stewart Coffin's Sunrise / Sunset (#181) Fit the 5 polyominoes into each side of the tray, making a symmetric pattern in each case. Gift from Bernhard Schweitzer (thanks!). IPP22	Stewart Coffin's Drop In (#153B) aka The Trap Fit the four pieces into the box through a small slot. They must be arranged so all fit within the inside perimeter of the box walls. Saul Bobroff IPP23	Stewart Coffin's Few Tile (#133) Made by John Devost A beautiful Padauk frame about 5.75" squared, with corner splines, and Birch plywood pieces. A gift - Thanks, John!
Stewart Coffin's Four Fit (#217) Made by Tom Lensch. Purchased from Tom at the Dartmouth College Mechanical Puzzle Day in Feb. 2008.	Stewart Coffin's Cruiser (#167) Made by Walter Hoppe.	Mind the Gap - Chris Morgan	Think Square - Pressman There are 4 small right triangles, 4 large right triangles, 4 stair-case shaped pieces, and 5 small squares. The pieces can be fit snugly into the tray with and without one of the five small squares.
Triadenspass - Logika	Pack It In - Great American Puzzle Factory 1996 Pack a set of 16 items into a suitcase frame. Flat cardboard pieces.	The Trapped Man - Tom Jolly Laser cut by Walter Hoppe. Five unusually convoluted pieces, including the little "man." The first challenge is to fit them into the tray so that none can slide or rotate. Next, try it with only four of the five pieces, then with only three! Several other puzzle goals accompany the Trapped Man puzzle.	Pac-Man - Milton Bradley First create 4 Pac-men with open mouths. Then use the same pieces to create 3 Pac-men with closed mouths. There are eye stickers on some pieces, which must be positioned correctly. The pieces can be flipped.
The Jayne Fishing Puzzle - A 1916 advertisement of Jayne's Tonic Vermifuge (yuck!). Discussed in Slocum and Botermans' "The Book of Ingenious and Diabolical Puzzles" on page 15. You were to cut out the fish and the ring and then pack the fish inside the ring. The fish names are (left to right, top down): Codfish, Shad, Red Grouper, Cowtrunk Fish, Flying Fish, Bluefish, Mackerel, Tarpon, Sheepshead, Moonfish, Striped Bass, and Weakfish. Also see No Fishing by Bepuzzled.		No Fishing - Bepuzzled 1998 Remove the water then fit all twelve fish into the bowl. AreYouGame has it. This is a nice wooden laser-cut, colorful, and faithful copy of the Jayne Fishing Puzzle of 1916.
In the Raging Rapids puzzle from Thinkfun (Binary Arts), you have to fit all the men into the raft, facing the right way. The figures' bases have various patterns of tabs and indents.	In the Mayan Calendar puzzle from William Waite, you have to fit all the glyphs into the tray, facing the right way. The glyphs have various patterns of tabs and indents. (Similar to Raging Rapids.)	Alex Randolph's Moebies - Springbok 1973 There are 8 sockets at various positions in the orange board. Six pieces and six pegs are included - the object is to find a way to peg the six pieces to the board so that all fit within the edges.	Springbok Fitting & Proper

Pack It In - Thinkfun This is "Conway's Curious Cube" which calls for three 1x1x1 cubes and six 1x2x2 blocks to be packed into a 3x3x3 box. There is only one solution - see this source.	Nine rhombic pieces fit in the tray. This is isomorphic to Conway's Curious Cube.	17 piece packing cube Another John Conway design. 5 of 1x1x1, 6 of 3x2x2, 6 of 1x2x4. Fit into 5x5x5. The same pattern should show on all sides. Gemani calls this "Made to Measure." I've also seen it as "Shipper's Dilemma."	Conway Box Deluxe This is a nicer version of the 17-piece Conway cube.
The Meiji Caramel puzzle is a version of Anti-Slide designed by William Strijbos. Pack 15,14,13, or 12 of the 15 1x2x2 pieces into the 4x4x4 box such that none can slide in any direction. There are no solutions using less than 12 pieces. Using 12 pieces there are only three solutions, but using 13 pieces there is only one solution. This puzzle won 2nd place in the 1994 Hikimi Wooden Puzzle Competition. Purchased from Torito.	36 piece Packing Puzzle	T Party - B&P	Loyd's Cube - Sam Loyd An IPP Puzzle from Jerry Slocum
L-Bert Hall Pack the nine identical pieces into a 3x3x3 cube seated in the box. Each piece is a concave tri-cube with holes and one dowel. This was designed by Ronald Kint-Bruynseels for IPP27, and made by Eric Fuller. The pieces are made from Cocobolo and the box is made from Lacewood.	Log Stacker - Elverson	Logs in a Box - B&P	Mmmm Pack the four M-shaped pieces into the box and close the lid.
Mine's Cube of Cubes Designed by Mineyuki Uyematsu in 2004. Exchanged at IPP24. 14 pieces pack into a 5x5x5 box. 2 solutions.

Nob's Never Ending Build a cube within the box, from 8 similar angled pieces. The one on the left is a rough handmade version - an auction win. I recognized this in a pic of Matti Linkola's exhibition, and found it on Trevor Wood's site. It is a copy of Nob's Neverending puzzle. Torito sells a version made by Himiki.

Make Room - variation of Stewart Coffin's #127, by Mr. Puzzle Australia Craftsman version in fine exotic woods - the box is a waxy wood called Yellow Leichardt. Four challenges: Pack all 8 blocks under the closed lid - 30 solns Pack 8 blocks plus the brass rod under the closed lid - 4 solns Pack 8 blocks plus the wooden dowel under the closed lid - 1 soln Shipping config - pack 8 blocks with the dowel through the hole in the lid - 3 solns

This is Tube-It-In by William Strijbos. (Photo from John Rausch's site.)

The Morph A cube dissected into four clever pieces can morph into three different solids to fill the compartments in the case. According to Bernhard Schweitzer, who sells a copy, this was designed by Boris A. Kordemsky of Russia. I believe this was issued by Bits and Pieces quite some time ago, but I am not sure. I found my copy on auction.

HABA Trickpack See my solution below.	Conway Packing Puzzle A gift from Brett. Eq. to HABA Trick-Pack.	3D Geometrex Rex Games Inc. San Francisco, copyright 2000 Sarcone & Waeber Gianni Sarcone described this puzzle in issue 52 June 2000 of the CFF newsletter, where he called it the Paradoxopiped. Start with nine pieces packed in the frame, then add the tenth. Gianni says "more than three solutions can be found."	18-Piece Mini-Cube-Block Puzzle Set
Bunchgrass Packing Puzzle "13/14" A box with 5 pieces made of spheres - the pieces fit in the box with or without a single sphere piece. They also can form a square-based pyramid. It is called the 13-14 puzzle since with the single sphere there are 14 pieces and 13 without.	For Your Own Sake - Hikimi (Japan) This puzzle poses the additional challenge of embedding 3 marbles.	Dragon's Eggs - Pentangle Find a way to pack everything into the box so that the three "eggs" are all concealed.	Slot Machine - Stewart Coffin #185 obtained from Henry Strout Build a cube within the box, fitting the pieces in through a small slot in the acrylic cover.
Third Degree - Bits and Pieces Designed in 1995 by Bill Cutler, who calls it the "3-Piece Blockhead." Discontinued.	Stark Raving Cubes / Sneaky Squares I bought mine from ISHI. Designed in 1983 by and still available from Bill Cutler. Awarded the Grand Prize at the 1986 Hikimi Wooden Puzzle Competition.	Three Pins By Jean-Claude Constantin. Fit the six pieces in two layers into the tray, aligning holes so that the three pins can be inserted, each through two pieces.	Four Square Fit the four dual-layer pieces into the tray.
Pack 6 - Eric Fuller Entered in the IPP 2003 Design Competition.		Sandwich - Vaclav Obsivac	HCP1 - Vaclav Obsivac
Brunnenspiel, by Markus Goetz	Malaga Box - Philos By Markus Goetz.	Mosaic - IQ Puzzles (Family Games)	Stack the disks to form a cob. This seems to be a copy of the Toyo Glass puzzle "A-Maize-Ing."
Something Fishy	Booze Crate	This is Packman by Gary Foshee. Get all of the elements into the cube so that all of its surfaces are flush. (Photo from John Rausch's site.)	A nice little packing puzzle handmade in the Ukraine. Purchased off eBay. I'm not sure, but I think this is the same puzzle as shown on www.golovolomki.ru in the Wooden Puzzles section, called "Disobedient Particles" by I.A. Nowitschkowa.
Dice Box - Sticks	Dice Box - Prisms	Trevor Wood's Cube the Square - unknown craftsman The 8 pieces form a 4x4x4 or an 8x8x1.	Nob's LL Puzzle - unknown craftsman Each of the 8 pieces is made from two L tricubes. They pack a 3x4x4 box, made from purpleheart.
Boxed LUV Stewart Coffin #189 a cheap Asian copy, but functional	Circelei - Hendrik Haak IPP26 Fit three hinged 3-layer polyominoes into three stacked trays.		Russian 3-piece packing Obtained from Rick Eason at NYPP 2008. The label is in Cyrillic and I cannot read it! I'm not sure, but I think this is the same puzzle as shown on www.golovolomki.ru in the Wooden Puzzles section, called "Pythagorean Trousers 2" by I.A. Nowitschkowa.
Oskar van Deventer's Two-Piece Packing From Bernhard Schweitzer at NYPP 2008

The Japanese company Toyo Glass issued a series of packing puzzles using glass elements (usually an assortment of plastic pieces which must be packed into a glass container).

Here are the Toyo puzzles I've got:

Packed in Tokyo I got this in Japan.

Java Tea [A]

Packing Peanuts [B]

Shot You

On the Rocks [A]

Here are some other Toyo packing puzzles, shown for reference - I don't have these unless otherwise noted. Much of the Toyo lineup has been re-issued by www.be-en.co.jp - a Japanese vendor. Puzzlemaster.ca carries them.

[A] means the Glass Puzzle Answer Book contains a solution.
[B] means a re-issue is available.

Pack the Beans [B]	Pineapple Delight [A] [B] Related to Pentominoes	Pack the Pudding (or Custard) [B]	Pack the Beer [B]
Pack the Plums [A] [B]	Pack the Peanuts [B]	A-Maize-Ing [A] [B] I have the Professor Brain's version shown above.	Pack the Rice Crackers [A] [B]
Pack the Orange [A]	Pack the Asparagus Designed by Nob Yoshigahara Related to Tridiamonds	Home Alone Husband	Bin Cross [A]

A regular polygon is a closed two-dimensional shape having some number of identical sides, joined at identical angles. They begin with the equilateral triangle, and proceed with the familiar square, pentagon, and hexagon, then continue with the perhaps less familiar heptagon, octagon, nonagon (or enneagon), etc.

Polyforms (Wikipedia entry) are pieces made by joining multiple copies of a given unit element which is a polygon. In the most straightforward cases, the unit elements are regular polygons and they are joined along full edges. These are also known as animals. The pieces can be distinguished by whether they are convex or non-convex. A piece is convex if you can join any two points inside the figure by a line segment that also lies entirely within the figure. Also, if a piece is distinct from its mirror image, it is chiral, otherwise it is achiral.

Polyforms can also be constructed using three-dimensional unit elements, such as cubes or spheres, and these are referred to as solid polyforms. Solid polyforms made from unit cubes are polycubes. Read about polycubes at The Poly Pages. When solid polyforms are constructed, some of the pieces will have all their unit elements lying in one plane, and others will not. The former are planar pieces, and the latter are non-planar pieces.

Two-dimensional polyform puzzles utilize some set of polyform pieces to create a given two-dimensional shape. Only three regular polygons can be used to tile the plane - equilateral triangles, squares, and hexagons. Naturally, most polyform puzzles have utilized pieces composed of such units, but other polygons can be used. Here are some of the better-known planar polyform types:

• Polyiamonds - (or n-iamonds) are equilateral triangles joined along complete edges. The term polyiamonds was coined by T. H. O'Beirne. See Jurgen Koeller's page on polyiamonds. Also see Ed Pegg Jr.'s page on iamonds.
• Polyominoes - (or n-ominoes) are planar shapes based on unit squares. The term polyominoes was coined in 1953 by Solomon Golomb, who has investigated them at length. Wikipedia entry here.
• Polyhexes are made from hexagons. See Jurgen Koeller's page on polyhexes.
• Polyaboloes or polytans, a term coined by Henri Picciotto, describe the forms made if a right-isoceles triangle (the shape you get when you divide a square along a main diagonal) is used as the unit polygon. Jurgen Koeller discusses polyaboloes, although the page is in German.
• Polydrafters (Wikipedia entry, Wolfram Mathworld entry) are composed of 30/60/90 right triangles (like a draftsman's triangle, hence the name, coined by Ed Pegg Jr.). See Sloan's sequence A056842. These shapes were used in the noted Eternity puzzle created by Christopher Monckton, and discussed here by Ed Pegg Jr. Polydrafters are also discussed by Bernd Rennhak.
• Polykites - Brendan Owen coined the term to refer to the pieces created from a kite-like unit that is a one-sixth section of a hexagon divided by the perpendicular bisectors of its sides. Read about polykites at Wolfram Mathworld. The Poly Pages include a section about polykites. Jurgen Koeller also discusses them.

The polyominoes start with a single unit, called a monomino. Two units joined along a full edge make a domino; three a tri-omino or tromino, four a tetromino, and five a pentomino. The set of all possible terominoes are the shapes used in Tetris. Note that the dominoes referred to here lack the patterns of a conventional set of dominoes, and as a rule, polyomino puzzles do not typically employ pattern constraints other than the occasional checkerboard coloring.

• translation - entails moving the shape within the plane while preserving a given orientation. In general translations are needed when computers are used to analyze such puzzles, to determine where a given piece can fit inside a grid, lattice, hull, or envelope, but translations are not important when enumerating physical pieces - all translations of a piece are considered identical.
• rotation - changing the orientation of a piece within the plane. Again, useful for computer analysis but usually all rotations are considered identical when enumerating physical pieces.
• reflection - flipping a 2D piece over to obtain its mirror image, or reflecting a 3D piece. This operation is sometimes legal, sometimes not, depending on the puzzle. Sometimes it is useful to know the total number of pieces including mirror images.

• free pieces - this is the number of distinct pieces excluding translations, rotations, and reflections. In other words, a given shape is free to move, turn, and flip in any way, so all such orientations count as the same piece.
• one-sided pieces - excludes translations and rotations but includes reflections. This is the count of interest if flipping a piece is not allowed, or if you're dealing with solid polyforms whose mirror images are considered distinct.
• fixed pieces - excludes translations but includes both rotations and reflections. (For those of a mathematical bent, free polyominoes are equivalence classes of fixed polyominoes under dihedral group D4.)

Enumerating Polyforms Sloan's sequences given for: # free . # 1-sided (holes allowed) Wolfram links at top show initial pieces; links in table to Wolfram, Ishino's site, etc. show all pieces
n, prefix	-iamonds #A000577 .#A006534 Wolfram	-ominoes #A000105 .#A000988 Wolfram	-hexes #A000228 .#A006535 Wolfram Wikipedia	-aboloes (-tans) #A006074 Wolfram Esser	-cubes #A038119 .#A000162 Wolfram	Comments
2 d[i]-	1.1	1.1	1.1	3	1.1	Dick Hess designed a puzzle using nine planar tridiamonds. The Naef Favus puzzle pieces are a set of planar and non-planar solid tri-diamond prisms. (Labeled dominoes are discussed in the Pattern section.)
3 tr[i]-	1.1	2.2	3.3	4	2.2	The two triominoes consist of one three-in-a-row and one "L" - the L is non-convex.
4 tetr[a]-	3.4	5.7	7.10	14.22	7.8	Tetromino sets: Tenyo BtC #783 See my diagram of polyhexagons up to tetrahexes. Naef's Hexagon puzzle uses the set of 7 free tetrahexes, made from metal nuts. The Snowflake puzzle by Stewart Coffin uses the set of three trihexes and seven tetrahexes. Michael Keller shows some figures and solutions made with the set of tetratans. The Eternity Delta puzzle is a commercial set of 14 tetratans. Kadon's Tan Tricks I includes 2 monotans, 3 ditans, and the 14 tetratans. Jurgen Koeller discusses tetracubes. The eight tetracubes are named: I O L T N, tower-right, tower-left, and tripod. They can make two boxes: 2x4x4 (1390 solutions) and 2x2x8. A set called Wit's End was produced by Lowe in 1967. Piet Hein's famous Soma cube uses the six non-convex tetracubes plus the single non-convex tricube.
5 pent[a]-	4.6	12.18	22.33	30.56	23.29 12 planar 17 non-p	Ishino's page on pentiamonds. Peri Spiele (Austria) makes a set of 19 n-iamond pieces packed into a Star-of-David tray. The set includes two tetriamonds, seven pentiamonds (all 4 possible + dups), six hexiamonds, three heptiamonds, and one octiamond. The planar pentomino pieces are named by convention after the letters they resemble: F I L N P T U V W X Y Z. There are too many commercial pentomino sets to mention. Ishino's page on pentahexes. Commercial sets of pentahexes: Tenyo BtC #22, Hi-Q Fusion, Hi-Q Confusion Kadon's Tan Tricks II includes the set of 30 pentatans. Stewart Coffin on solid pentominoes;  Stewart Coffin's Unhappy Childhood puzzle Kadon's page naming the planar pentacubes;  Kadon's page naming the non-planar pentacubes
6 hex[a]-	12.19	35.60	82.147	107	112.166	Ishino's page on hexiamonds. Hexiamond sets: Tenyo BtC #6 Hexomino sets: Tenyo BtC #600, Spear's Multipuzzle George Miller sells a set of 82 hexahexes. Kadon's Tan Tricks III includes the set of 107 hextans. Kadon sells a set of 166 hexacubes. Livio Zucca's Sexehexes
7 hept[a]- sept[a]-	24.43	108.196	333.620	318	607.1023	Ishino's page on heptiamonds. Heptiamond sets: Tenyo BtC #24 Kadon sells a set of 108 heptominoes. Peter Esser's page of the 108 heptominoes.
8 oct[a]-	66.120	369.704	1448.2821	1116	3811.6922	Kadon sells a set of 66 octiamonds. Ed Pegg Jr.'s page on octiamonds. Kadon sells a set of 369 octominoes.
9 non[a]- enne[a]-	160.307	1285 .2500	6572 .12942	3743	25413 .48311	George Miller sells a set of 160 noniamonds.
10 dec[a]-	448.866	4655 .9189	30490 .60639	13240	178083 .346543
11 endec[a]-	1186 .2336	17073 .33896	143552 .286190	46476	1,279,537 .2,522,522
12 dodec[a]-	3334 .6588	63600 .126759	683101 .1364621		9,371,094 .18,598,427

Perhaps the best known variety of polyominoes are the Pentominoes. Hexominoes and Heptiamonds are also used in puzzles, but the number of pieces quickly becomes unwieldy as one goes up from there.

Basic pentomino challenges include fitting the pieces into a rectangle, or a square with some holes. You can also form large models of each pentomino!

If you become bored with the basic pentomino puzzles, several people have devised more interesting challenges...

• Eric Harshbarger's Enclosures
• The K.S.O. Glorieux Ronse school pentomino project has wonderful problems to solve. Click on the "Records" menuitem.
• The Bridge Challenge - abut the pentominos along full edges in an arc to build a bridge with the largest area under it.
• Pieter Torbijn Pentomino Tetromino Challenge - Using a set of tetrominoes and a set of pentominoes, create the longest 1-unit-wide enclosed continuous corridor.
• The 20 Problem - find sets of 3 that allow you to make 3 congruent shapes.

Often Pentominos are presented as a packing puzzle, but they are very versatile. If they are made from unit cubes, they can be arranged either flat or in 3 dimensions. However, the 3-d constructions do not really interlock due to the limited size and convolution of the pieces.

Concept 5	Yasumi	University Games Pentomino Set
Logika	Kohner Hexed (thick and thin versions, and alternate cover)
Pentomino sets made into games:
ZahlenLabyrinth - Logika	Camelot (castle pieces on top of flat pentominos - arrange the pieces to build the castle)	Springbok Pentominoes

The 12 planar pentominoes can be fit into various rectangles:

• 3x20 - 2 solutions
• 4x15 - 368 solutions
• 5x12 - 1010 solutions
• 6x10 - 2339 solutions, found in 1960 - 911 equivalence classes; see Wilfred J. Hansen's paper on equivalence classes.
• 8x8 square with a central 2x2 hole - 65 solutions

The 12 planar solid pentacubes can be packed into various boxes:

• 2x3x10 - 12 solutions
• 2x5x6 - 264 solutions
• 3x4x5 - 3940 solutions

See Chapter 3 in Stewart Coffin's The Puzzling World of Polyhedral Dissections.

Here is one of the 3x4x5 solutions, in case you need to put your set back in its box...

I I I I I   X F N L L   Y Y Y Y T
X V V V T   X F N L T   X F Y Z T
U F N V P   X F N L P   U Z Z Z T
U W N V P   U W W L P   U Z W W P

Wit's End by Lowe from 1967 is a set of tetracubes. The instruction sheet gives several construction problems.	The Spear's Multipuzzle is a plastic set of hexominoes. It includes all 35 "free" hexominoes and duplicates of 7 of them. The pieces are essentially 2D - they are not built from unit cubes and cannot be built into 3D structures. The set comes with a 6x10 tray and a booklet of problems specifying subsets of pieces to be fit into the tray.
The Ten Yen puzzle, published in 1950 by the Multiple Products Corp. of NY, includes a monomino, domino, both trominoes, and 3 each of the tetrominoes and pentominoes. Kadon offers one. Pieces in three colors. One challenge is to create identical shapes from the sets of three different colored pieces.
A gift from Brett of three "Meiji Chocolate" plastic Polyomino puzzles by Hanayama - Milk (12 pentominoes), Black (11 hexominoes), and White (8 pieces) - find them at Kinokuniya.

Tenyo made several polyomino puzzles in their "Beat the Computer" series. Here is a link to a site showing most of them. I have obtained some of them:

#0

#22 A set of the 22 pentahexagons.

#600 This is a set of the 35 hexominoes.

#783 783 comprises two sets of the tetrominoes.

The first two are copies of Tenyo #6 and #24, made by Lucky. #6 is a set of Hexiamonds - each piece is formed from six equilateral triangles. #24 is a set of Heptiamonds - 7 triangles each. Torito sells a black set of Heptiamonds from Tenyo. Peter Pan made a set of Hexiamonds.	Hi-Q Fusion is, like Tenyo #22, the set of 22 penta-hexagons. So is another version, Hi-Q Confusion.
Kwazy Quilt by Kohner is equivalent to Beat the Computer #0. I have two versions - thick pieces and thin pieces. There are several versions including Hi-Q Euclid by Gabriel. When circles are arranged into a hexagonal grid, there are triangular interstices. The Kwazy Quilt pieces include all of the ways a circle can be augmented with from one to six triangular interstices, plus an extra "single."	This "Wisdom Puzzle" includes only seven of the Kwazy-Quilt-type pieces. Select one and place it in the upper left hand "Begin" position. Then try to fit in the rest. 120 combinations in total.
Peri Spiele (Austria) makes a set of 19 n-iamond pieces packed into a Star-of-David tray. The set includes two tetriamonds, seven pentiamonds (all 4 possible + dups), six hexiamonds, three heptiamonds, and one octiamond.	I saw this variation from "Peri" on someone's web site - I do not have this puzzle. It uses 19 pieces but not full sets.

A one-million pound prize was offered for the solution of the Eternity Puzzle. I didn't win. The puzzle comprises 209 pieces called 12-polydrafters. For more info on the Eternity series, take a look at Miroslav Vicher's site Ed Pegg's site	The Eternity Delta puzzle was billed as a warm-up to the full Eternity. It uses the set of 14 tetratans. Here are some interesting sites discussing polytans: Henri Picciotto Tetra-tans - Michael Keller Wen-Shan KAO Kadon Ed Pegg
This is the Eternity Meteor puzzle.  It uses a set of ten penta-hexagons.	Last but not least, the Eternity Heart.

I believe this is "Hextra" from Robert Longstaff Workshops. It uses a set of septa-hexagons. This is a gift from Carol Monica, the proprietress of one of the best puzzle shops around - the Games People Play shop in Cambridge, Mass.

The Snowflake puzzle was designed by Stewart Coffin (#3), and this version made of foam was offered by Binary Arts in 1993. It includes two sets of 3 tri-hexagons and 7 tetra-hexagons, a tray with two levels, and a booklet of challenges.

Here is an unnamed but colorful set of tetra-hexes in a clear case.

The "Hexagon Sense-A-Gone" is one in a series of Brain Drain puzzles from Mattel. It employs a set of 3 tri-hexagons and 7 tetra-hexagons. The pieces cannot be flipped, and only one of each of the pairs of mirror images is used. The pieces are prettily colored and suggest 3-dimensional cubes, but the instructions do not indicate any edge-matching constraint. Assemble them / Pack them in the tray.

This is as good a place as any to show the six Mattel Brain Drain puzzles from 1969 (that I know of)...

Hexagon Sense-A-Gone Assembly	Profound Round Circle Dissection	Mangle Quadrangle Edge Matching
Checkle Heckle Checkerboard Dissection	Block Shock Edge Matching	Square Where Packing Equivalent to the Pressman Think Square puzzle.

Kadon Rombix

Galt Puzzle Blocks

TriPentaHexagon - George Miller

Piet Hein's Soma Cube is the classic example of the polycube puzzle. The Soma Cube uses the six non-convex tetracubes plus the single non-convex tricube. Pictured above are: a pair of plastic Soma cubes from Parker Brothers; a wooden Soma on an aluminum base - the wood is beautiful - dark and striated - I believe it's Rosewood; the green felt base is stamped "Produced in Denmark" though some of the text is damaged; a Soma Cube I made from Lego; Skor-Mor's Fascinating Cube. Read about the Soma Cube on: Jurgen Koeller's Soma page Thorleif's Soma page Christian Eggermont's Soma page The Balanced Soma is an assembly such that the pieces remain together when balanced on a single cube placed at the center of the bottom face. At least six such constructions exist.
The eight pieces of this Baumeisterspiel ("Master Builder") set from Logika include the Soma pieces, plus a 1x1x3. I also have a "mini" version with a handy cover.	Rhoma is like Soma, but with rhombic pieces. I have a large and a small Rhoma.	The Illusions from Magnif is similar to Rhoma.
Mellow Yellow - Not Too Hard (1142 solns) OK Orange - Somewhat Hard (30 solns) Mean Green - Fairly Hard (16 solns) Rough Red - Really Hard (1 soln) Baffling Blue - Extremely Hard (8 solns) Perfect White - Incredibly Hard (1 soln) There was also a brown, identical to the Red. The Impuzzables line of 3x3x3 polycube puzzles were some of the earliest introduction I had to mechanical puzzles. I was able to purchase more on a vacation trip to the Great Smoky Mountains. Here is a link showing the pieces of the Impuzzables. The Impuzzables are also described on p. 3^3-13 of Kevin Holmes' and Rik van Grol's book "A Compendium of Cube-Assembly Puzzles using Polycube Shapes," which also discloses the number of solutions for each. I have seen them for sale at bgamers.com (Games Unlimited in Pittsburgh PA).
Bill Cutler's Splitting Headache yields a nice A-Ha moment when one solves it systematically.	Stewart Coffin's Half Hour Cube (#29)	The TetraCube
The Bedlam Cube	Metropolis	The Pedestal Problem has cubies joined at an offset, and must be assembled inside fenceposts
The craftsman Scott T. Peterson of the state of Washington made this beautiful version of Stewart Coffin's Unhappy Childhood (#41) puzzle for me. Of the 17 non-planar solid pentominoes, 12 lack an axis of symmetry. Eliminate the two that fit into a 2x2x2 box to arrive at the ten pieces of this puzzle. Those ten pieces pack into a 2x5x5 box in 19,264 ways, and can be checkered in 512 ways. Only one of those possible checkerings has a unique solution (one other has no solution and the rest have multiple solutions) - this is the checkering for the Unhappy Childhood.
Cube from Melissa & Doug - the same set of planar pieces as the Diabolical Cube (see Kevin Holmes' Compendium page 3^3-3)	Obsivac Cube 3	Rubik's Bricks
Naef Gemini Designed by Toshiaki Betsumiya. Ten pieces, each made from two 1x2x2 blocks. See the Gemini pieces here. See a comprehensive list of Naef puzzle designers here.	Stewart Coffin's "Patio Block" (#82) made by IP.	Obsivac Cube 1
Naef Campanile Designed by Manfred Zipfel and Cordula von Tettau in 1979. See the Campanile pieces here.	Flogik.de Skyscraper This is almost identical to Naef's Campanile (but made with much less quality). In the Skyscraper, piece 'B' has an extra cubie sticking up at the junction.	Professor Brain's Tower Puzzle 10 pieces, different from Campanile.
	Here is a puzzle using pieces made from unit spheres - the pieces stack inside a cage. It is called "Cerebrum."
Closterman cube Six pieces fit sequentially into a cubic cage. Nicely handmade in Yellowheart wood.	Here is another set of pieces in a cage. I received this puzzle in a trade with P. F. Ramos - he designed it and IP made it. It is called "Twin Pentominoes Into a Light Box." There are two instances of each of the non-planar pentomino pieces.	Double Cross" (without the tray) (discontinued) from William Waite. Fit the 6 pieces together in 2 layers of 3. I think I actually prefer it without the tray - the pieces mate tightly and seem like they would be difficult to manipulate if they were in a tray.
The Triangle Cube aka Pantene	Pairs of Prisms Ergatoudis IPP13 exchange	Hexahedroom This very nice puzzle was made by Eric Fuller, from Ebony and Jatoba woods. Form a cube within the box by fitting the pieces in via the available holes. A cool solution. Based on an IPP25 exchange from Hirokazu Iwasawa.
Naef Escalon Designed by Jost Hanny.	Jamaika - by Markus Goetz	Eclecticube - Kevin Holmes
The L-Ements series by Rick Eason. Seven L-Ements IPP25 Eight L-Ements Nine L-Ements IPP23 See Ishino's page on the Nine L-ements puzzle.
Tetris Cube Designed by Matt Campbell, produced in 2007 by Imagination Games and tetris.com. 9839 solutions - confirmed by BurrTools. This is the small-sized cube.	KeshIQ erasers mfd by Seed Co. in Vietnam. Purchased from Eureka	Octix - Trigam
The Jeu du Cube and L'Enervant puzzles are vintage French non-cartesian cube dissections. (I believe Le Tracassier is also the same set of six pieces.)		Double Take - Mag Nif 2003 Eight pieces form a 4x4x4 cube or an 8x8 square.
Dollar Tree Hexagon Equiv. to Naef Favus at a fraction of the cost! (Favus was designed by Toshiaki Betsumiya.)	Japanese hexagon An Asian version of the Hexagon/Favus.	3 Pyramid Cube by Philos
The 3456 Pythagoras Puzzle from Pentangle challenges you to use the nine pieces to form a set of three cubes 3x3x3, 4x4x4, and 5x5x5, then add them together and form one 6x6x6.	Trevor Wood's Prism Cube - unknown craftsman Made from highly figured canarywood.

There are several interesting polycube puzzles I do not have:

• 25 Y pieces will pack into a 5x5x5 cube (1264 solutions)
• 25 N pieces will also pack a 5x5x5 cube (4 solutions - see Torsten Sillke's site).
• 11 F pentacubes will pack into a 4x4x4 (with holes): see Ishino's site.
• Cotway's Cube - six N tetracubes and three monocubes make a 3x3x3

Assembly puzzle pieces need not be made just from unit cubes used in pieces to build a yet larger cube - spheres are another common building block, as are tetrahedral shapes. It seems that vendors like to associate Egyptian mythos with tetrahedrons, not the more realistic square-based half-octahedrons.

The three Gordon Brothers pyramids are some of my favorites - the smaller Perplexing Pyramid is doable by hand, but I wrote a computer program to solve the Giant Pyramid. The Big Pyramid has a square base. You can purchase the Giant and Perplexing, as well as a set called "Warp-30," from Kate Jones at Kadon.

Here are some solutions:

Perplexing Pyramid 3 OO = 1 OOO = 2 OOOO = 3 4 3 4 OO = 4 OOO = 5 OOO = 6 O O O 5 4 5 3 6 5 1 5 1 6 6 6 3 2 2 2	Giant Pyramid 5 L = 1,2,3,4 C = 5 5 S = 6 3 3 P = 7 I = 8 7 J = 9 3 5 2 2 5 7 3 1 2 6 1 4 6 9 1 7 7 6 2 6 8 4 4 4 8 9 9 9 1 8
Big Pyramid 1 OOOO = 1 2 1 OO 8 2 OO = 2,3,4 2 4 1 OO 4 2 5 O = 5,6 8 5 5 OOO = 7,8 6 6 3 1 O 6 4 3 3 4 8 7 3 8 7 7 7

See another solution to the Giant Pyramid, on Richard Whiting's site.

The classic 2-piece pyramid has to be one of the most simple yet elegant puzzles devised. Once you've solved it, it gets old, but it is always fun to watch a newbie's first encounter with it.	Rosie's Puzzle - Drueke The classic 2-piece has also appeared with each piece divided again.	This pyramid by Pussycat has 3 identical unusual (and pointy!) pieces.
Tut's Tomb by Mag-Nif is a 4-piece classic. The German company Pussycat makes a diminutive equivalent version. A similar puzzle, in steel and having six pieces, was offered by Bits and Pieces.
This is another Tut's Pyramid, by DanleyQuest. The objective is to construct a pyramid using the four large pieces. However, each piece has different symbols on its faces, and an additional goal is to ensure that each of the three visible faces of the pyramid will have three specific symbols that signify a certain phrase.		This four-piece tetrahedron called Tetra Teaser by Stokes Publishing Co. uses the same piece shapes as the DanleyQuest model, but without the symbols or mythos.
I have a 6-piece puzzle that forms a tetrahedron. Its white pieces are all planar and are equivalent to the pieces of Piet Hein's Pyramystery.	Piet Hein's Pyramystery (I don't have this.)	I do, however, have this plastic version of Pyramystery, by Hubley.
Here is a 4-piece puzzle called "Der Fluch des Pharao" (Curse of the Pharaoh) by Markus Goetz, made by Philos and purchased from Funagain Games. The pieces actually do interlock but I still categorize this as an assembly rather than an interlocking puzzle.	Cubikon Ball Puzzle The pieces of the Ball Puzzle from Cubikon are all planar and have spheres joined at 90-degree angles. Contrast with the pieces of Fantastic Island which employ 60-degree joints. Fit the pieces in the tray, then use subsets of them to make pyramids.	Kanoodle - SmartGames Fit the pieces in the tray, then use subsets of them to make pyramids.
The Bermuda Triangle is a wooden pyramid - the pieces do not interlock.	This is a Step Pyramid from Philos, designed by Ferdinand Lammertink, having 10 pieces.	Here is another step pyramid, from Germany. It is much smaller than the Philos, and made of plastic rather than wood. It uses 7 pieces.
This is a ten-piece pyramid. No name or manufacturer info on the box, other than "Mindgame." Purchased at New England Hobby. There are at least two distinct solutions, since I found one by hand that is different from the supplied solution. The pieces are composed from two logical units - a square-based pyramid, and a tetrahedron (slightly stretched). There are a maximum of two tetrahedrons and 3 pyramids per piece.		Dalloz Tempil - from the John Ergatoudis collection.
This is Pyrra. It has 3 distinct solutions.	Dollar Tree Pyramid (Richard's pic)	I got the PyrPlex and the OrbSticle from Andy Snowie (CalmPlex).
This is a Pyrix puzzle. Assemble a tetrahedron such that each face is a uniform color, constrained by the fixed threading of the pieces. U.S. Patent 5108100 - Essebaggers 1992	From the same maker as Pyrix, Pyram consists of an octahedron and four smaller tetrahedrons, each having various patterns on their faces. Build a tetrahedron satisfying a pattern constraint.	The Pyrus Puzzle completes the three offered by Enpros. Like Pyram, an octahedron and four tetrahedrons. Build a larger tetrahedron having each of the four colors appear on every side.

There are various styles of dissection puzzle, but all of them involve some figure which has been cut up, or "dissected." The objective is usually to re-assemble the figure. Sometimes the pieces of a dissection are contrived such that an alternative figure can be assembled, too. In some cases, it is even possible to "hinge" the pieces to each other so that both forms can be assembled. See this link at Wolfram for more info on dissections.

The Tangram puzzle is a venerable classic where the real objective is to form various silhouettes from the given pieces. However, this version from Melissa & Doug is presented as a straightforward square-dissection and tray-packing problem.	The Magic Square Make a square from the four identical pieces. According to Frederickson (p.30), this was designed in 1873 by Henri Perigal, who was a London stockbroker and amateur mathematician (1801-1899).	Square Up Make a square from the four identical wooden pieces. The pieces come arranged with a small square hole in the center - your task is to find a way to make a square containing no hole.
Double Square - Thinkfun This is another fairly well-known design - form a square from 4 pieces, then add a fifth piece (a small square) to form another larger square. This design dates back at least as far as the 1934 Johnson Smith catalogue.	The St. Charles Milk Puzzle Seven pieces form a square. Discussed in Slocum and Botermans' The Book of Ingenious and Diabolical Puzzles on p.12.	Dickinson's Witch Hazel A vintage advertising promo.
The Elusive Square Puzzle - TSL Twelve pieces, whose collective area is 32 unit squares. What does that tell you about the solution?		Snider's Diamond Puzzle The 10 pieces form a square. Discussed in Slocum and Botermans New Book of Puzzles on p.14.
This design has been around for a while and has been called the Egyptian Puzzle. Assemble a square from the 10 pieces that result from 5 smaller squares each sliced on a bias from a corner to the midpoint of an opposite side. It is discussed on p.19 of Slocum and Botermans' "Puzzles Old & New." The Horse Blanket Puzzle was used as advertising for blankets made by Wm. Ayres & Sons of Philadelphia. This twleve-piece version was used to advertise Devoe Paint. Note the kite-shaped pieces resulting from a couple of squares being doubly-sliced. This cardboard version from 1943 is called "Bombing Mystery." Mystic Wedge by the Crestline Manufacturing Co.of Santa Ana CA. 20 equal right triangles (10 black, 10 red) make a square. Derive this one by first cutting each of the five squares in half into equal rectangles, then dividing each rectangle along a main diagonal. Dicksinson's Seed Ten Card Puzzle - 1910 Another variant of the Egyptian puzzle, similar to the Devoe 12-piece, but some right triangles have been fused to form two isoceles triangles. (I don't have this.)

Super Star - Melissa & Doug This is a dissection of a five-pointed star, in a tray.	Broken Heart Form a heart from the 9 pieces.	Doctor's Puzzle Board
IQ Circle (PeToy Hong Kong)	Mind Bender Circle	Squaring the Circle - Dollar Tree
Perfect Squares	Profound Round One of Mattel's Brain Drain series.	Fit the six pieces into the case to form a rectangle such that it contains only 3 straight seams. From puzzle-factory.com.
Form a six-pointed star using the six pieces. Also from puzzle-factory.com.	This set of "What's Your Score" puzzles from Shackman includes a dissected cross, square, and form a star.	Watney's Red Barrel puzzle Build a red barrel from the pieces. A nice symmetric dissection.
"Jeu de la Croix" is a vintage French boxed version of a dissected cross on a pedestal.	"La Cocotte" is a vintage French boxed puzzle - form a bird shape from eight isoceles right triangles.	Bibendum six-piece rectangle
"Jeu de l-Octogone" is a vintage French boxed dissection of an octogon into 12 pieces. (I don't have this.)	The "Red Cross" or "Mysterious Cross" puzzle has been issued by several manufacturers of different nationalities and is known by various names. The eight red pieces form a Greek cross. The eight white triangles fill in the corners of the square.	IQ Mega-Form Circle
The Land Puzzle You are given a 2x2 square, with one corner unit square missing, leaving three unit squares. Cut the shape into four identical pieces.	Stacked Triangles - George Miller	Stacked Squares - George Miller
Spear's Shape Puzzles

The dissected T has certainly been the most popular, but other letters have been dissected, too.

Missing T - Thinkfun This is a version of the classic 'T' dissection, by Thinkfun.	Another classic T.	Pa's T from Drueke.
This cardboard version of the classic T dissection puzzle is a promotional item for a magician.