While similarly playing brio with a two year old, I thought about a different dimension not mentioned here - super loose tolerances make the search space really weird.
In true 2-year-old fashion, my kid would bend the rules as much as possible by literally forcing pieces to the edge of their tolerance to make things fit that shouldn't fit. 8 piece circle yea, cool, but with a sufficiently old brio set handed down for 40 years or whatever, you can totally make a 7 piece "circle" thing.
So I decided some day I'll craft an interview question out of that, to see if people can figure out a good way to map a set of pieces laid out with given tolerance ranges for piece, see if it can connect, etc. Haven't thought about it enough to really polish it for an interview, but some day.
A heuristic could try all kinds of fun force-directed placement stuff. For an exact solver, I think your best bet would (unfortunately) be to finely quantise the possible positions and orientations of each piece, describe each piece by 2 sets of positioned unit vectors (the vectors in one set start at the centre positions of each "hole" and are directed towards the centre of the piece, the other set is similar but holds the "plug" positions and orientations), and say that a partial solution is feasible iff every "plug" position is sufficiently far from all other plugs, and either sufficiently far from all other holes or within some small tolerances (in terms of both distance and angle) of some other hole. Actually, you would probably also need to treat the piece body as a "nothing else can occupy these positions" constraint. I say "unfortunate" because the position and orientation grids would need to be very fine relative to the size of the pieces, leading to a large state space thus long running times.
I think it would be fun to look for solutions that maximise the "badness" (e.g., sum of distances between matched holes and plugs) :)
My son was really into Brio trains when he was young, and I wrote a program to visually design layouts by placing track segments one after the other. The program took that tolerance into account, and gave a score to the layout based on how much it had to force the pieces together. I had the idea of adding some automation to design complex networks but that never materialized.
I did cover it and had a toggle for it in the visualisations but decided to cut it out because the article was long enough already. There's maybe still a reference to the "vrio system" lurking in it.
My understanding -- correct me if wrong -- is that this hugely complicates things because the search space expands so much. If you imagine three straight pieces in a row, with vrio they now form a fan of possible positions. Then with corners and so on you have a near infinite amount of wiggle room. To do it accurately you probably need to map out the physical space a given connector can move within, but for the visualisation I just loosened the "connectors must align" rule to be "connectors must be within 6mm of each other", which is wrong but fairly close.
One of them used constraint solving with Z3, which was indeed reasonably fast. However, by far the fastest was a simple backtracking solver written in Rust which used bit twiddling to quickly test for intersections. For polyomino's in particular, this represents between 10x and 100x constant speed boost, depending on the size of board. There's no way to get that back with a smarter solver.
Had something similar to this with the kids with Lego Duplo tracks, similar topology but the switches gave the system state. Going "backwards" through a switch set the train to return that direction when coming the other way.
So we had a goal to make the train do interesting behaviors, like cover the entire track autonomously, pushing the switches itself. The biggest run I remember was a 4 bit counter.
Kid is now entering his last year of CS + Maths degree, so I guess it checks out.
> When this solver backjumps, it forgets the failure as soon as it lands, so if the same dead end comes up in a different part of the search it gets rediscovered from scratch.
Modern solvers such as CP-SAT combine some SAT features with a CP solver, based of the work of Peter Stuckey I think.
The strongest insight here is that the SAT solver did not merely solve the same problem faster. It solved a better-formulated problem: choose the pieces as well as their placement.
My three year old taught me something he saw on a YouTube video: you can search through a maze and find your way out just by keeping your right hand on the wall at all times and continuing till exit. Does a DFS.
Another nifty maze solving trick: Using flood-fill in Paint or some such, starting at the entrance, paint the wall on one side of the entrance red, and the other blue. You'll find that the border between the red and blue sections (the path where one wall is red and the other is blue) is the path to the exit. If there are loops, then you'll end up with uncolored squares, but you can just treat those as blue if you follow the red edge.
I'll be honest, while it's possible the article is genuine,at some point I felt/realized it seemed like an ad for the book, and made the story feel like it was not genuine and more like a contrived example of why the book is so useful and not real (again, not claiming real vs not real,just the vibe I felt) so I stopped reading.
Insidious "gift" idea: A set of wooden track pieces with lengths and join angles chosen such that no subset of them can form a closed loop. No matter what you try, it's always just a little bit off.
This attempt at humble bragging about how smart your two year old is was not necessary for this article. There does not need to be a constant game of trying to 1 up other parents by bragging about how much farther ahead your kid is compared to others.
If the comment from the 2yo correcting him about oblong vs. oval wasn't enough to trip your satire detector, 'graph with two cycles' should have blown it up. And now I realize that your comment 100% had to be sarcasm and I'm a fool for responding. At least I didn't downvote
Incredible. My two-year-old forgets to include Lambek when lecturing on Curry-Howard-Lambek correspondence. Kids.
While similarly playing brio with a two year old, I thought about a different dimension not mentioned here - super loose tolerances make the search space really weird.
In true 2-year-old fashion, my kid would bend the rules as much as possible by literally forcing pieces to the edge of their tolerance to make things fit that shouldn't fit. 8 piece circle yea, cool, but with a sufficiently old brio set handed down for 40 years or whatever, you can totally make a 7 piece "circle" thing.
So I decided some day I'll craft an interview question out of that, to see if people can figure out a good way to map a set of pieces laid out with given tolerance ranges for piece, see if it can connect, etc. Haven't thought about it enough to really polish it for an interview, but some day.
I immediately got nerd-sniped by this...
A heuristic could try all kinds of fun force-directed placement stuff. For an exact solver, I think your best bet would (unfortunately) be to finely quantise the possible positions and orientations of each piece, describe each piece by 2 sets of positioned unit vectors (the vectors in one set start at the centre positions of each "hole" and are directed towards the centre of the piece, the other set is similar but holds the "plug" positions and orientations), and say that a partial solution is feasible iff every "plug" position is sufficiently far from all other plugs, and either sufficiently far from all other holes or within some small tolerances (in terms of both distance and angle) of some other hole. Actually, you would probably also need to treat the piece body as a "nothing else can occupy these positions" constraint. I say "unfortunate" because the position and orientation grids would need to be very fine relative to the size of the pieces, leading to a large state space thus long running times.
I think it would be fun to look for solutions that maximise the "badness" (e.g., sum of distances between matched holes and plugs) :)
>if people can figure out a good way to map a set of pieces laid out with given tolerance ranges for piece
so you work in some space where extremely good visual understanding and ability to abstract in 3 dimensions is a prerequisite?
My son was really into Brio trains when he was young, and I wrote a program to visually design layouts by placing track segments one after the other. The program took that tolerance into account, and gave a score to the layout based on how much it had to force the pieces together. I had the idea of adding some automation to design complex networks but that never materialized.
I did cover it and had a toggle for it in the visualisations but decided to cut it out because the article was long enough already. There's maybe still a reference to the "vrio system" lurking in it.
My understanding -- correct me if wrong -- is that this hugely complicates things because the search space expands so much. If you imagine three straight pieces in a row, with vrio they now form a fan of possible positions. Then with corners and so on you have a near infinite amount of wiggle room. To do it accurately you probably need to map out the physical space a given connector can move within, but for the visualisation I just loosened the "connectors must align" rule to be "connectors must be within 6mm of each other", which is wrong but fairly close.
> a good way to map a set of pieces laid out with given tolerance ranges for piece, see if it can connect, etc.
Märklin C track needs this.
That tolerance turns a clean combinatorial problem into a continuous one
Why would that be a good interview question?
So far as I can figure, it would not haha. There's a reason why it's still just a hypothetical on my backburner of interview questions
But you have to think about something after hours of brio.
I wrote several polyomino solvers for this project:
https://www.oranlooney.com/demos/soma-forest/
One of them used constraint solving with Z3, which was indeed reasonably fast. However, by far the fastest was a simple backtracking solver written in Rust which used bit twiddling to quickly test for intersections. For polyomino's in particular, this represents between 10x and 100x constant speed boost, depending on the size of board. There's no way to get that back with a smarter solver.
Had something similar to this with the kids with Lego Duplo tracks, similar topology but the switches gave the system state. Going "backwards" through a switch set the train to return that direction when coming the other way.
So we had a goal to make the train do interesting behaviors, like cover the entire track autonomously, pushing the switches itself. The biggest run I remember was a 4 bit counter.
Kid is now entering his last year of CS + Maths degree, so I guess it checks out.
Similar article I read 10 years ago that covers some of the same ground, with some pretty SVG's as well.
http://strangelyconsistent.org/blog/train-tracks
Yon should publish this on LinkedIn.
Given my feelings about the quality of the... discourse... on LinkedIn, I can't tell if this is a genuine compliment or a fiercely backhanded one.
> When this solver backjumps, it forgets the failure as soon as it lands, so if the same dead end comes up in a different part of the search it gets rediscovered from scratch.
Modern solvers such as CP-SAT combine some SAT features with a CP solver, based of the work of Peter Stuckey I think.
The kid doesn't seem to be doing any actual teaching here. Cool that a two-year-old can say "exponential", though, I guess.
> “Dada! Degree three. No Euler circuit.”
…Oh. Okay, fine, weird rhetorical device but you do you.
The strongest insight here is that the SAT solver did not merely solve the same problem faster. It solved a better-formulated problem: choose the pieces as well as their placement.
My three year old taught me something he saw on a YouTube video: you can search through a maze and find your way out just by keeping your right hand on the wall at all times and continuing till exit. Does a DFS.
This only works for two dimensional mazes where both the entrance and exit are on an edge and there are no loops in the maze.
If you introduce a bridge, or a tunnel, or put the goal in the middle, you can get stuck in a loop.
Another nifty maze solving trick: Using flood-fill in Paint or some such, starting at the entrance, paint the wall on one side of the entrance red, and the other blue. You'll find that the border between the red and blue sections (the path where one wall is red and the other is blue) is the path to the exit. If there are loops, then you'll end up with uncolored squares, but you can just treat those as blue if you follow the red edge.
Throw a loop/island in the maze and see how your kid reacts.
A nice case of an algorithm being easier to learn physically than abstractly
I vaguely recall a windows screensaver that did this
Once I got the battery powered Brio train, it became more fun for me than the kids
Hilarious article. Surprised to see so many people missing the joke in the comments.
I'll be honest, while it's possible the article is genuine,at some point I felt/realized it seemed like an ad for the book, and made the story feel like it was not genuine and more like a contrived example of why the book is so useful and not real (again, not claiming real vs not real,just the vibe I felt) so I stopped reading.
> I'll be honest, while it's possible the article is genuine
No, there's not really much chance of that:
>> “Dada, real planners use SAT and its relatives for timetabling, chip layout, and routing for the same reason.”
Sometimes you have to prove you’re #1 Dad.
What year was your son born? Nobody has said “Silly Billy” in 30 years, unless under the auspices of a duly appointed official.
I associate that phrase with Dr. Henry Killinger
https://youtu.be/9FUik3QotBQ?si=27AcY47wLNov0Vzw
I'm pretty sure the Angry Dishwasher Man has said it.
Insidious "gift" idea: A set of wooden track pieces with lengths and join angles chosen such that no subset of them can form a closed loop. No matter what you try, it's always just a little bit off.
brio sets are for children 3 years and older...
That kid must be a genius then!
This attempt at humble bragging about how smart your two year old is was not necessary for this article. There does not need to be a constant game of trying to 1 up other parents by bragging about how much farther ahead your kid is compared to others.
If the comment from the 2yo correcting him about oblong vs. oval wasn't enough to trip your satire detector, 'graph with two cycles' should have blown it up. And now I realize that your comment 100% had to be sarcasm and I'm a fool for responding. At least I didn't downvote