BLOKL MINI - Building Blocks, Puzzles and Games

I have always been a fan of toys and games that are affordable and portable. This project is inspired by KANOODLE a tiling puzzle that costs About $10 and fits in a pocket, backpack or other travel bag. It is sort of like a pentomino puzzle but not really, some of the pieces are made from four and three "balls" rather than five. Also it doesn't have free play building block capability. BLOKL MINI provides enough linking cubes to make a pentomino puzzle, a Soma Cube and have blocks left over to play games or make whatever you want.

Tools

1. Side cutters
2. Super Glue (brush type works best I think)
3. Clothes or embossing iron

Materials

1. 1cm Linking Cubes - I like these best - https://www.lakeshorelearning.com/products/math/math-manipulatives/linking-centimeter-cubes/p/LL879/
2. Pencil Case - I used https://www.sterilite.com/product-page.html?product=17226W12

You get a lot of cubes for about $40, 1200 in 10 colors. I sorted out cubes on sort of an improvised way to make five kits but what you need for one BLOKL MINI is -

1. Pentomino - 5 each of all ten colors and then and additional 10 of white. There are only 10 colors but there are 12 pentomino pieces. We are going to color two pieces made from white cubes.
2. Soma Cube - 4 each of Red, Orange, Yellow, Green, Blue and Black. Three Brown.
3. Free play blocks/linking cubes - a handful or two. You can also do a couple more Soma Cubes. Some of the puzzle solutions have interesting similarities and having more than one can be interesting.

The Soma Cube is my favorite puzzle and mathematical object. Lets make one.

We are going to use the color code developed by mathematicians Conway, Guy and Guy for the SOMAP-a map of the 240 unique solutions of the Soma Cube puzzle. You'll need

1. 3 brown cubes
2. 4 cubes of each of red, orange, yellow, green, blue and black

1. Place a dab of glue on the pegs of two of the brown cubes
2. Connect the cubes together to form a Vee
3. Use side cutters to trim off the one remaining peg
4. Using a clothing or embossing iron on high heat, press the peg cut blemish/bump against the iron for 1 to 3 seconds. It may take a couple of tries but you be able get pretty nice cleaned up cube face. You may need to spend some time with the iron you have to dial in your process.

The L, T and Z build is very similar to the V.

Dexter? Dexter is Latin for "right" and this piece can be considered to be "right handed". Similar to building the V and then adding a fourth linking cube. Just make sure the fourth cube lines up with your right hand's thumb like I show in the last pic above.

Sinister? Sinister is Latin for "left" and this piece can be considered to be "left handed". Similar to building the V and then adding a fourth linking cube. Just make sure the fourth cube lines up with your left hand's thumb like I show in the last pic above.

This piece is the most symmetrical so it is called the Crystal. It is also a bit trickier to build.

1. Glue two linking cubes together at their faces that do not have peg holes as shown in the first two pics above.
2. Let that pair sit for a minute to make sure the glue is set up.
3. Glue two more linking cubes on to the pair made in step 1.
4. Trim off the two extra pegs.
5. Use the iron to smooth off the blemish from the peg trim

I call this one the "Geode" because it cleaves roughly into two halves that are symmetrical. The three piece portion can be rearranged in four different ways by flipping and twisting the "double Z" formed by Dexter and Sinister and then dropping in the "L." Another two solutions can be made by a complete rearranging all three. Six of the two hundred forty unique Soma Cube solutions are essentially a three piece puzzle.

Those same three pieces do exactly the same thing in another arrangement of the T,V,Z and Crystal. I discovered a little bit about the two "Geodes" through just playing with the cubes but it also led me to use a visual drag and drop computer programming language from Berkely called SNAP! with and added Graph Theory capabilities. More about this in Step 15 "Mathematics and Computer Science Activities."

So twelve Soma Cube solutions

Pentominoes are another classic puzzle - all of the shapes that can be made joining five squares at their edges. We are using cubes so we are joining at faces instead of edges but we are keeping all the cubes in the same plane.

1. The twelve pieces are shown in the first picture. Note there are only ten colors of linking cubes. White is the easiest color to color over so that is why there are three pieces made from white or white/pink linking cubes.
2. Build the pieces as before with a little bit of glue, then trimming off spare pegs and smoothing with the iron.
3. I recommend coloring one piece with a light blue crayon and the white/pink with purple. The crayons are also handy for recording solutions. Cell phone pics work well also though.

Two pentomino puzzles. The 8 x 8 is the easier of the two because the four untiled squares are allowed anywhere except the out edge or perimeter. The 6 x 10 is much more difficult, there are 2339 unique ways to do this I have only found two of them on my own.

Lots of great information on pentomino tiling here - "Pentominos" https://isomerdesign.com/Pentomino/

The 8x8 tiling example I mentioned above is from - "Rosetta Code - Pentomino Tiling" - https://rosettacode.org/wiki/Pentomino_tiling

The handful of linking cubes that fit into the pencil case in addition to the pentominoes and Soma Cube(s?) are great for building cube based shapes like Minecraft. You can also make game pieces for your own custom chess set. I am fond of simple chess variations. Here is an example 5x5 chess card game in Scratch - "King's Castle Pokémon Chess" https://scratch.mit.edu/projects/908209590/

Another game I like is "BLOK TOK!" for two or three player -

1. Everyone starts with five cubes
2. Each player connect their cubes together to make a shape
3. Take turns drawing one additional cube and adding to shapes
4. If someone decides that the shape they have made is "a thing" they declare "BLOK TOK!"
5. The "thing" they have made now becomes the first clue of a game of "20 Questions" (https://en.wikipedia.org/wiki/Twenty_questions)
6. If someone guesses correctly what the thing is that round is over. Continue playing until all blocks are made into shapes.
7. If no one declares "BLOK TOK!" before all of the linking blocks are used up that round of the game is over.

I am a big fan of crayons in general. The 16 color pack from Crayola matches the pentomino piece colors nicely.

1 cm grid paper is handy for documenting puzzle solutions and making custom game boards.

You can get some here that you can print - https://www.webtools.services/paper-template/1cm-graph-paper-printable

or here (I buy cubes from them too so ...)

chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.hand2mind.com/media/contentmanager/content/gridpaper.pdf

Some very interesting mathematical concepts can be explored using the Soma Cube and Pentominoes.

1. "Equivalence Classes Among Pentomino Tilings of the 6x10 Rectangle" - https://www.cs.cmu.edu/~wjh/papers/hexclass.html
2. "Rosetta Code - Pentomino Tiling" - https://rosettacode.org/wiki/Pentomino_tiling
3. "Mining the Soma Cube for Gems: Isomorphic Subgraphs Reveal Equivalence Classes"-https://scholarship.claremont.edu/jhm/vol12/iss2/28/
4. "The complete "SOMAP" is found"-https://www.fam-bundgaard.dk/SOMA/NEWS/N030518.HTM
5. "Graph and Group Theoretic Properties of the SOMA Cube and SOMAP"-https://scholar.rose-hulman.edu/math_mstr/185/
6. https://snap.berkeley.edu/ - "Snap! is a broadly inviting programming language for kids and adults that's also a platform for serious study of computer science."
7. https://snapapps.github.io/edgy/ - "Edgy is a block-based programming language ...It provides a hands on interface to manipulate graphs...Edgy is powered by both Snap! ...and JSNetworkX to both visualize and provide functionality to work with graphs.