How about a jigsaw puzzle for children's day. This is one of the classical thinks that can be done on a laser. This how-to will guide you through constructiong the tiles in xcs, so you can add a picture of your choice.
This example here is 110mm x 100mm with 36 tiles, each tile 15mm x 15mm. But you can use the same technique that is described here for larger jigsaw puzzles.

Note: This project requires a honeycomb and air assist for perfect results. Triangular prism will not work here.
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Step 1

First we create a rectangle of 110mm x 110mm on layer 1. We name this layer Outer Frame

Step 2

Now we create the base of the tiles on the second layer which we name squares for now. We use squares with a size of 15mm x 15mm for this which are arraigned in rows and columns. But we only draw half of the rectangles. If you imagine a chess board we only draw the black fields, not the white ones.

I prefer to enter everything by numbers instead of painting this. So we draw 18 rectangles of 15mm x 15mm at the following positions:

10mm/10mm

40mm/10mm

70mm/10mm

25mm/25mm

55mm/25mm

85mm/25mm

10mm/40mm

40mm/40mm

70mm/40mm

25mm/55mm

55mm/55mm

85mm/55mm

10mm/70mm

40mm/70mm

70mm/70mm

25mm/85mm

55mm/85mm

85mm/85mm

Step 3

Now we add the missing lines at the outside on a third layer named "lines". These are horizontal lines with a length of 15mm at the positons

25mm/10mm

55mm/10mm

85mm/10mm

10mm/100mm

40mm/100mm

70mm/100mm

and vertical lines

of 15mm at the positions

10mm/25mm

10mm/55mm

10mm/75mm

100mm/10mm

100mm/40mm

100mm/70mm

Step 4

We now have something like a raster. But if you look closely you are able to differ between “real squares” and “fake squares” (that are created by four surrounding squares or lines). To make this a little bit more easy to see, you can select the square layer and change the settings to raster engrave. XCS will now paint the “real squares”.

Now it is time for the connections between the tiles. We can take 5mm circles for those. Each edge between two squares need a connection. So we need one circle per edge. A circle is placed at any position along the edge, either about 75% of the circle inside a “real square” and 25% outside (later this is a gap) or 75% outside and 25% inside (later this will be a pin). I decided to have gaps and pins in two layers which makes it easier to differ them later.

Please vary the position of the circles on the edge slightly to get unique tiles.

Step 5

From now on it is important to apply these steps exactly. If you do the geometric operations in the wrong order they will not produce the desired results.

We start with the gaps. Select a “real square” and all the circles that are gaps for this tile. Select the substract function in the geometric operations menu. Note: It is important to select all gaps at the same time. With the current version of XCS it will not work if you try this one by one. Repeat this for every “real square”.

Step 6

Now we have to go through all real squares again. Select one and all pins for this square. Select the add function from the geometric operations menu. Repeat this for every “real square”.

Now you should have the typical jigsaw layout ready for cutting. Some of the tiles will be in the circle layer. Select them and move them to the square layer again. So you should have three layers left now. The outerframe, the squares and the lines.

The provided xcs file in this how-to is exactly this stage of the construction as this is the difficult part.

Step 7

Now we import an image for our jigsaw puzzle. I prefer to have it a little bit bigger then the tiles to help the user during construction of the puzzle. I took an svg from Pixabay but you could use any other picture that you like. Pay attention that there are not too many blank tiles as this will increase the difficulty. 

Step 8

Laser everything. It is a good idea, to do this layer by layer. I started with the picture at 180mm/s, 90%, 1 pass, then the squares at 5mm/s, 90%, 1 pass, then the lines at the same setting and finally the outer frame also at the same setting.

Here you should not use the triangular prisms. Some tiles could fall between the prisms and will be damaged, when the laser cuts the neighboured tiles. Either place the wood on another piece of wood or something else (which will result in fumes at the bottom side) or place it on a honeycomb.

In the photos you see what can happen with triangular prisms. That was my first attempt.

Step 9

Optionally you could do a second jigsaw where you use vector engraving (scoring) for the squares and lines. This can be glued bellow the outer frame as a guide where which tile belongs. This makes it a little easier to build the jigsaw puzzle so I would recommend this for younger children. For older ones I would just cut a 110mmx110mm piece and glue this behind the frame. 

Design Files
Puzzle.xcs
4weekscontest
week1
toy
gift
plywood
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