My two year old taught me constraint solving

Summary

Reading on email? The visualisations will work better in browser. My son is two years old, which means he has an Apollonian will to power and loves all kinds of mechanised transportation and earthworks machinery. His particular joy is “playing choo-choo” with a Brio wooden train set. Since he likes me to be involved, but I am expressly NOT permitted to touch the trains, I amuse myself by building interesting track layouts. After a long while, I began to think more systematically about Brio. The pieces are clearly designed to fit together into shapes, so what’s the underlying structure in the design? Given out set of pieces, what is the most elaborate layout I can build? I don’t have a formal maths background, but I could see that this was an interesting algorithms problem lying on the floor in front of me. As I explored this, my son demonstrated a hitherto undetected expertise in constraint solving. The rest of this post is a lightly editorialised account of what he told me. The Brio system Brio is a wooden train toy for kids but has been documented in depth by particularly interested adults. I first turned to the unofficial Brio track guide, which gives every piece a letter code and a measurement. A is the 144 mm medium straight. A1 and A2 are 108 mm and 54 mm variants. E is the standard curve, an eighth of a circle, measuring just over 182 mm on the inner edge and 222 mm on the outer. Eight of those 45-degree curves therefore enclose a circle about 40 cm across. Most pieces can be flipped over, so a curve can bend left or right depending on how you arrange it. A simple Brio layout You get ramps and bridges too, but let’s ignore them and treat the system as two dimensional for simplicity. This suits me because the bridges are quite rickety and my son keeps knocking them over, so I try to hide those pieces. First, make the track close One morning I begin by putting eight curves together to form a circle. “Circle!” my son cheers. Good! Reading Shapes with Thomas the ...