Giant Zendo Stone Bean Bags

Introduction
With the introduction of 8x scale Icehouse pyramids there is now a need for other similarly scaled games pieces and boards. For a game of 8x Zendo, in addition to the pyramids, large "stones" are also needed.

Latest News: I finished 35 Marking/Answer stones and 22 Guessing stones. They were all made using basically these directions. Scroll to the bottom of this page to see some pictures.

Note: I wrote these directions after making three or four prototypes. I might slip between what "was", what "is", and what "will be" or "should be". I might also change between general "good ideas", including ideas I've had since purchasing the initial batch of materials, and the specific decisions I made for the prototypes without warning. Sorry about that.

Requirements
Let's look at the exact requirements for these "stones":

• There needs to be a way to mark whether a koan exhibits the budha nature or not. These "Marking Stones" should...
  • Be to basically the same scale as the pyramids.
  • Be able to show one of two colors. This can be done by having two different Marking Stones or by having a single type of Marking Stone that can show two different colors.
• There needs to be a way for the master and students to perform Mondos. "Answer Stones" should...
  • Be able to be hidden in a player's outstretched hand.
  • Should be the same (or otherwise obviously matching) colors as the Marking Stones.
• There needs to be a way to keep track of the number of mondos a student has gotten correct and, therefore, the number of rule guesses that a student has accumulated. "Guessing Stones" should...
  • Merely exist. That's it; they have no real physical requirements. However, to make the game more aesthetically pleasing and to make the state of the game more obvious to outside observers, it would be nice to have the Guessing Stones pretty much the same size and shape as Marking Stones but a different color.

Design decisions

• Marking Stones: The standard small glass bead normally used to mark Zendo koans is somewhere around .5 to .75 inches in diameter. Scaled up to 8x, this means that we need something around 4 to 6 inches across. A hunk of glass 4" in diameter poses various logistics and cost problems. An alternative that Alison Frane suggested (and other subsequently kicked around) was the use of bean bags. To keep the total number of bean bags down, they can be made white on one side and black on the other (to keep with the traditional black/white color scheme). So we're looking at disc-shaped bean bags that are, let's say, 4.5" in diameter. To make construction easier, they can be made octagonal rather than round. They should not be stuffed so full that a lot of the bottom side shows when it's sitting on a flat surface. Experiments have shown that about half a cup of dried beans just about fits the filling requirement. What is the maximum number of marking stones that could be possibly be used in a game of Zendo? Let's see, one for the null koan, 24 for the 24 different possible single-pyramid koans, and 20 for 20 two-pyramid koans that would use up the remaining pyramids. That makes an absolute maximum of 45 marking stones used in a single game. But you could probably get away with a mere 36.
• Answer Stones: It's a little tough to hide a half-cup, 4.5" bean bag in a single outstretched fist. It's even tough to keep it it hidden using two hands. There are a few solutions to this and each group is welcome to use whichever they feel most comforatable with:
  • Use the Marking Stone bean bags enclosed in two hands. So what if someone else sees how you are going to guess during a mondo? The only information they'll get is what another student thinks, not the master.
  • Use the Marking Stone bean bags initially hidden behind the students' backs and displayed with some sort of "1-2-3-Shoot" thing.
  • Use standard 1x (.5 - .75") glass beads from a regular game of Zendo.
  One Answer stone is needed for each player (incl. the master). This would be a maximum of, what, 7?
• Guessing Stones: So that outside observers can see how many Guessing Stones each player has accumulated, these should probably be bean bags of similar construction as the Marking Stone bags, but in a color (or multiple colors) other than black on one side and white on the other. Theoretically, there is no maximum number of Guessing Stones that can be used in a single game. For the sake of argument, let's say three each of six students.

Materials and Tools

• Fabric: A good strong cotton duck seems like the best bet. Prototype bags were made from a good sturdy poplin and they turned out ok too. One clever idea is to make the two sides of the Marking/Answer Stone bags two fabrics that feel different. That way a student can pick a side of a Marking/Answer Stone while holding the bag behind his back. The length of fabric needed depends on its width. Each "row" of bean bags requires 5.5" of the two different materials (or 10" of a single material). You can get 9 bean bags per row out of 54" wide cloth or 11 per row out of 72" cloth. So, to get 45 bean bags out of 54" cloth, you'll need 5 rows, or at least 27.5" each of black and white. It wouldn't be bad to increase this to at least 30" to allow for some slop.
• Ballpoint Pen: Whatever type of marking tool you use, make sure it won't bleed through the fabric.
• Thread: Don't skimp. Get good strong thread, because you don't want a bag splitting during a game. You could even use quilting thread if it fits through your machine.
• Needle: For hand-sewing that last seam.
• Sewing Machine: You only have to sew plain old straight lines, so any machine will do.
• Beans: Any dried beans will do. Navy beans are good. Or maybe dried peas. Those dried soup mixes in a plastic bag are too expensive. You'll need about a half cup of beans per bean bag. That means you can get about four bean bags per 1 lb. bag of beans. Before you go out and buy 15 lb. of navy beans, however, make a few Marking Stones and see how far a single bag of beans really goes.
• Bean Funnel: If you already have some type of funnel with a narro holethat's about .5" in diameter, that'd be great. If not, you can just roll a piece of paper into a cone and use that. Believe me; you DON'T want to fill a bean bag one bean at a time.
• Special Ruler: This is the thing that makes the whole process go a LOT smoother. Get a piece of thin wood (1/8") or cardboard, cut it down to about 9" by just under 5.5". Then mark it as shown in the diagram below. This custom "ruler" makes all the measuring quick and painless.
  
  The table below shows where to position each of the marks along the edge of the ruler. The second column shows the positions used for the prototype bags with are 4.5" side-to-side and made with a .5" seam allowance, while the third column shows the general formula (just in case you want to make ones in a different size).
  
  

  side-to-side diameter	4.5	d
  seam allowance	0.5	s
  (calculated value)	0.932	z = tan(22.5deg) * d/2
  (calculated value)	1.318	y = d/2 - z
  ruler width	5.5	d + 2s
  ruler length	at least 8.682; 9 inches would do.	at least 2d + 2s - y
  E'	0.5	s
  F'	2.318 (or a very little over 2 5/16)	y + 2s
  A	3.182 (or a very little under 3 3/16)	d - y
  B	5.0	d + s
  C	5.5	d + 2s
  D	6.364 (or a little under 6 3/8)	2d - 2y
  E	6.864 (or a little under 6 7/8)	2d + s - 2y
  F	8.682 (or a little under 8 11/16)	2d + 2s - y

  
  The trick here is that you want to mark both sides of a 5.5" wide strip of cloth at once. That way the marks on the the two sides can't become mis-aligned. Nifty, huh?

Process

1. Cut the black and white fabric into 5.5" strips (so that you end up with strips that are 5.5" x 54" or 72".
2. Sew pairs of strips (one white and one black) together, "right" sides facing, with a half-inch seam allowance.
3. Use the ruler to mark seam end points.
   • Turn the ruler 90degrees and line what was the bottom of the ruler up with the left edge of the fabric. (The corner of the ruler should be at the corner of the fabric, and Points E' and B on the ruler should be right at the long side seams.) Mark points F' and A.
   • For the first set of marks, line the left edge of the ruler up with the left end of one of the strips and mark all eight points E' through F. Be sure to mark all the points along both edges of the strip.
   • For subsequent sets of marks, just slide the ruler down the strip of fabric so that points E' and F' on the ruler match up with marks E and F on the fabric from the previous set of marks. Heck, while you have th ruler in this position, you can go ahead and draw a dotted D-D line.
   • Draw the connecting vertical and diagonal lines connecting the marks along the two edges. You can use the ruler as a guide to figure out which marks to connect. The C-C and D-D lines are for cutting, so make those dotted lines. Go ahead and use a ballpoint pen right on the fabric. Don't worry, you'll be drawing on what will be the inside of the bean bag.
4. Sew along all of the the A-F (and F-A) and E-E lines. DON'T sew the B-B lines.
5. Cut along the dotted C-C and D-D lines. You can also cut next to the diagonal A-F seams leaving a half-inch allowance. You should end up with an octogon that's still unsewn along one edge.
6. Turn the octogon insideout. Here's an easy way.
   • Loosely fan-fold the octogon into a zig-zag as viewed from the unsewn edge.
   • Gently "peel" the "lips" of the unsewn edge back over the rolled up fabric.
   • Now peel/fold the loose unsewn edges and try to push the folded up fabric between them.
   • Keep peeling and pushing until you get the whole thing turned insideout.
7. Use the funnel to fill each bean bag with about a half cup of beans.
8. Fold the unsewn edges into the bag and blind stitch the seam (line B-B) together. (A "blind stitch" is exactly the same as a "ladder stitch". Go to this link for more information.)
9. Make all the two-color bean bags first before going on to the single-fabric ones. When making single-fabric bags, start with a single strip of fabric 10" wide (2d+2s), fold that in half (right side touching), and sew the side away from the fold, leaving a half-inch seam allowance. The only 'problem' is that the marks on the that fancy schmancy ruler are off now. Well there's two ways around that:
   • Trim half an inch from the top (as it's shown in the diagram above) of the ruler.
   • Make a second ruler that's only 5" wide with points F', A, and F on one side of the ruler offset by half an inch from what's shown in the table (A to the right, F' and F to the left.
   With this modified ruler, you should be able to mark and make the bean bags as described above. Just keep the 'modified' edge of this new ruler against the folded edge of the fabric strip.

Done
Spiffy, ain't they?