## Introduction: Layerd Shadow Puzzle: the Cave

> How to play

Our cave consists of three layers. Put ‘isosceles right triangles’ on each layer to match the given picture on the base floor.

> How does it work?

The triangles are the same size, but when they become shadow, their size can be different!!! HOW?

As the name Layered Shadow Puzzle suggests, the secret lies in “three layers” where you put the triangles. The Cave uses the principle of the relation between ‘the distance of light and object’ and the size of its shadow. The shorter the distance between them, the larger the shadow becomes. We've set the perfect distance between 1st, 2nd and 3rd layer which makes the ratio of size of shadow of each floor(1st, 2nd, 3rd) = 1 : 1.414….(square 2) : 2, so that n st floor’s triangle’s hypotenuse exactly matches n+1 st floor’s triangle’s base line. (see the picture)

> The shadows from all the pieces are combined to form a certain shape like a cat, a star and so on. Since the triangles may have various colors, when they reflect on the bottom floor, it looks so beautiful! The puzzle just becomes an ART!
> Our cave is for people who want to get away from simple puzzles and enjoy multi-dimensional puzzle fully using and understanding the scientific principle and the beauty of shadow. Please enjoy it!!!!

> Check out the pictures to see how The Cave has evolved

## Step 1: Make the Basic Structure(4 Pillars and a Ceiling)

> What you need:
1) four wooden sticks - the base side: 7mm*12mm / length: 265mm
(Actually the base doesn't necessarily have to be exactly this big, but our blueprint follows it.>
2) a 5mm wooden board bigger than 172mm*160mm
3) a rubber hammer

> Step 1-1: Make the slots where the acryl layers can sit later.
Engrave three 6mm*2mm rectangles on each wooden stick. To make shadow get bigger at a fixed ratio(1: square root 2) at each layer, the distance between three slots is the most important. From the top, make the slots at the point of 115mm - 41.5mm - 58.5mm-50mm. Be aware that 2mm has to be counted when engraving the stick. For the elaborate cutting we recommend you use the lazer cutting machine.

> Step 1-2: Cut the wooden plate for the ceiling.
Please refer to the blueprint here. Rectagles on the apexes are the holes for the four pillars(Step 1-1) to be put. A circle at the center is where the lighting would be located. Two lines are the space for the roof.

> Step 1-3: Join the four pillars to the ceiling.
Hold a rubber hammer, treat a pillar as a delicate nail and drive pillars into the four holes on the ceiling. Be careful that the pillars are put from the top.

> Step 1 is complete now!

## Step 2: Make the Roof and the Lighting

> This is an optionalstep.
You can just use your smart phone flash light, without making the roof with a separate lighting.

> What you need:
1) a 5mm wooden board
2) a super glue
3) one small electric light: The smaller it is, the better for the convenience. But it should be bright enough too. It was really hard for us to find a proper one, try your best! :D

> Step 2-1: Print out the pieces and assemble them.
Please refer to the attached blueprint to make the pieces you need. When you are done with cutting the pieces, now what you have to do is to assemble it like a cube! If they don't fit tightly, the super glue will help you. Assemble them to make the shape of a lid.

> Step 2-2: Attach the lighting.
Attach the small lighting under the roof with super glue. Check if the bulb works properly.

## Step 3: Fit the Acyrl Layers Into the Slots & Glue the Walls

> What you need:

1) Three 1 mm*15 cm*15 cm acryl plates
2) Two wooden (open) walls
3) Super glue (again)

> Step 3-1: Prepare three 1 mm*15 cm*15 cm acryl plates.
According to our blueprint it can be a bit thicker than 1 mm, but shouldn’t be bigger than 15 cm*15 cm unless you fix the size of the ceiling first.

> Step 3-2: Insert each of the three plates to the four slots of each layer. (Picture No.1).
Don’t worry if the acryl plates are not in perfect line with the pillars, since they will find the right place when you glue the walls.

> Step 3-3: Prepare two wooden structures as the attached blueprint.
They should work as open walls supporting the pillars and plates altogether, making The Cave more prettier.

> Step 3-4: Glue them to two pillars each.

> Step 3-5: If you find the heights of the wooden walls and the pillars differ too much, you can grind them off with a grinder or sandpaper to make them even.

## Step 4: Make the Floor

> What you need

1) Rectangular wooden sticks with a small slot engraved on it.
2) A wooden board thinner than the slot on the wooden stick of 1)

> Before starting Step 4: The reason for making making the floor separable?
The reason for making the floor separable is to widen the player’s experience by enabling to put The Cave upside-down and project the final image to the ceiling. If you don’t need this, you can just make a simple floor with a piece of wooden board and glue it to the pillars and walls right away.

> Step 4-1: Prepare three wooden sticks
For the length of each sticks, please refer to the attached blueprint. They are going to be connected to the pillars and walls, and work as three sides of the floor.

> Step 4-2: Prepare the wooden board of the proper size. This is going to be the floor.
Prepare the wooden board, considering the size of the retangular space you can make with the three wooden sticks of Step 4-1. Here don’t forget to take into account the depth of the slots as well. The board must be able to fit into the 3 slots.

> Step 4-3: Glue the three wooden sticks.

> Step 4-4: Glue the connected wooden sticks to the pillars and walls of Step 3.

## Step 5: Varnish (if You Want)

You may varnish if you want, but we didn't.

## Step 6: Cut Out Triangle Pieces

> Step 6: Make the pieces
What we suggest is making pieces as small as possible so that you can play with as many pieces as possible at the same time. (But of course it should be big enough to control.) According to our experience, isosceles right triangle with sides of 2 and 2*square root 2(cm) worked well.

Acryl pieces of various colors will make the final shadow more fascinating, while wooden pieces-you can recycle the remnants from other steps- will give you a complete vivid black shadow.

## Step 7: Print Out the Puzzle on Paper or OHP Film

> Step 7: Print out the puzzle
Print out the puzzle so that you can place it on the floor as a real-size guidance. We originally thought of using OHP film because it enables you play the puzzle while still being able to enjoy the design of wooden floor. But printing it on a normal white paper is also possible. This way, the colors of projected shadows are more vivid compared to the projection on the wooden floor.

Or you can try to solve the normal 2D tangram puzzles, too. Although the pieces are all the same size and shape in The Cave, you can still generate the same final image with various combinations.

Also, try designing your own puzzle instead of printing out the ones already made. Think of The Cave as less of a puzzle but more of a canvas, where you can create your own image using different colors of triangles. Of course, you can make your own pieces other than triangles. (It doesn't even have to be acryl really.)

## Step 8: Enjoy It!

> Step 8: Play!
Finally, with all the parts of The Cave assembled and the puzzle ready (optional), turn on the flash light of your smartphone and place it carefully on the ceiling. You can still use the roof(light box) we've previously made. But since the intensity of the light we used (1w) is not strong enough, smartphone flashlight is far better if you intend to play The Cave in the daylight. (Still, the small light works well enough in darkness.)

At first we chose this LED because it was flat enough to easily hide under the roof-we didn’t want this toy to be overly large and take up too much space. However, if you want a brighter lighting, you can modify as you want. Just don't forget to adjust the height of the roof as well.

Please be sure that the flash light is placed on the exact center so that the light is not hindered or distorted.

## Step 9: Optional: Play the Cave Upside-down

Optional: Play The Cave upside-down (It's what the Step 4 was all for!)

You can also turn The Cave upside-down and project the light to the ceiling. Be careful not to turn it with the pieces still on the layers since they will all drop down. Instead, turn the body upside-down first, and then place the pieces as normal. This way, you can use The Cave as a shadow-casting light and widen your experience to the real ceiling!