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As further proof of my unsuitability to be a child minder (see previous post) I found myself playing with an Ikea LILLABO 20-piece basic set train.The train set has 16 pieces of track (12 curves, two straight pieces and a two part bridge) and 4 pieces of train.
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If you contact IKEA corporate, they will most likely follow your advice and add a few more pieces to increase the number of possible looping maps. The small difference there is that the paths can overlap in arbitrary ways, but it's the same sort of path-routing fun.
If they already included an extra 2 pieces of track to form 18 different layouts, and then a engineer found out that by reducing the track size by 2 the end user could still create an amazing 9 different layouts. There are heaps of parents out there who think their job ends when they hand over a toy - that's where it begins.

I assume I can adapt it to work with Tomica's Plarail, which are incredibly popular here with many nice trains. Thereby reducing the for every 10 kits they made they'd essentially get another one built for free without the customer every really noticing. And that's not even including the reduced cost of storage, price of shipping, or square footage in the retail environment. Here's a picture of the 9 different layouts.The picture was generated using a little program written in Processing. The bridge is red, the straight pieces are green and the curves are blue or magenta depending on whether they are oriented clockwise or anticlockwise. The curved pieces can be oriented in either way.To generate those layouts I wrote a small program which runs through all the possible layouts and determines which form a loop.
Especially when the enjoyment will most likely go unnoticed by the end user, in this case a 5 year old kid.

The program eliminates duplicate layouts (such as those that are mirror images of each other).It outputs a list of instructions for building loops. These instructions contain 15 characters C (clockwise curve), A (anticlockwise curve), S (straight piece) and B (the entire bridge). Here are the building instructions for all the shapes in the picture above:AAAACCAAAASSAABCCCCCCSSAAAAAABCAAAAACASSAAAABCAAAAASCASAAAABCAAAAASSCAAAAABAAACAACAAASSAABACAAAASACSAAAABACAAAASSACAAAABAACAAASSAACAAABPS You can actually create more possible layouts than these because the Ikea pieces have a lot of play in them and can be abused to form other shapes. But where's the fun in that?PPS Ikea can actually double the fun by adding just two more pieces. C # o f # # To calculate the angle to the tangent at point s (the angle c), # note that the angle formed by os and the tangent is a right angle # (since os comes from the centre of the circle).

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