Updates and a New Utilities Puzzle
This week, after actually taking most of independence day off, I put some more work into exploring kinds of short easy-to-produce videos. It's easier to produce work that takes advantage of existing work, and who better to borrow from than myself?
One thing on my list is to remake the original doodling in math class videos, available with a maximum resolution of a stunning crisp 240p, in HD and also with some small changes (especially in the first one, where I did not know what I was doing at all).
Many people have never seen the originals since they're so low quality, and when I was putting together what I might want to sell on a DVD, it was shocking to be reminded how low res the earliest videos are. So I've edited the first couple scripts and should be able to produce them pretty quickly with the originals as a guide, except they will be much better all around and the first one even has an alternate ending.
The second easy video, which I hope to have out early next week, is a response/late-collab that comes with a puzzle solution and referencing some other folk's work.
Have you heard of the utilities puzzle? It's a classic and very googleable, if you haven't. Basically the goal is to draw lines connecting each of three utilities to each of three houses, without any lines crossing.
I was invited to do a collab about a variation on it last fall with Grant Sanderson of 3blue1brown where it's on a mug, but their timeline was too short to work out for me. Here's his video: https://www.youtube.com/watch?v=VvCytJvd4H0
And what the mug looks like, copied from the mathsgear website:
But then I thought, hey, never too late to participate! Especially since no one in his video came up with my solution, or the more general solution!
So here's my variation on the puzzle, to give you a chance to work it out for yourself before I finish and post the video :)
The Vi Hart Infrastructure Special: In addition to making non-crossing lines from each utility to each house, every house should connect to every other house with internet lines, and every utility station to every utility station with a separate secure network, all with no crossings. So basically, make everything connect to everything, that’s 15 lines, three each for gas, water, electric, social network, and secure network, and no line crosses any other line. On a mug.
Have fun and see you next week!
Vi
Comments (13)
Never seen the utilities puzzle on a mug! The discrete mathematician in me (which essentially coincides with just me) loves it. It of course reminds me of the seven-color torus my wife crocheted for me.
Ooh so cool!
Wow, would be awesome to re-watch all the original videos and get my 4 year old into these.
Are you going all George Lucas in your original vids? Can we expect a CGI Dewback in the background? 😂
For Vi’s version, I made four trips through the donut hole. Can it be done with fewer?
Can’t you squeeze one of those around the cup handle...?
So... I happen to own this genus 3 surface... <a href="https://imgur.com/a/MQEMp9Z" rel="nofollow noopener" target="_blank">https://imgur.com/a/MQEMp9Z</a> Wonder how many houses you could do with that
Ooh, what a fun object!
Now I want a coffee mug with intricate wiring that makes music :)
Here is my poorly rendered ascii solution: ┌────────────────────────────────────────┐ │ MUG │ │ ┌──────────────────────────────┐ │ │ │ ┌─────────────────────┐ │ │ │ │ │ ┌───────────┐ │ │ │ │ │ │ │ ┌───┐ │ │ │ │ ├────┬─┴┬───┬─┴┬───┬─┴┬───┤ │ │ │ │ │ │ ┌──┴─┬┘ ╱└─┬┘ ╱└─┬┘ │ H │ │ │ │ │ │ │ │ ╱ │ ╱ │ │ O │ │ │ │ │ │ │ │ ╱ │ ╱ │ │ L │ │ │ │ │ ├─┘ ┌─┴┬───┬─┴┬───┬─┴┬───┤ E │ │ │ │ │ ├────┴─┬┘ └┬─┘ └─┬┴───┤ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├──────┘ │ │ ┌──┤ │ │ │ │ │ │ │ │ │ └───┘ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ └─────────┘ │ │ │ │ │ └──────────────┘ │ │ │ └────────────────────────┘ │ │ │ └────────────────────────────────────────┘ Is there any way to add formatting to comments here?
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Ok I found a mug with enough white space. I think I got it. If you call the houses 1,2,3 and the utilities A,B,C. Use the handle as the bridge, connect 1 to A, B to 2, 3 to C. Then between the existing lines, connect 1 to B, 2 to C. Still using the handle, 3 wraps to A. Next, connect 3 to B by going direct shortest path diagonal line. Same thing, 2 to A. Then 1 goes across the half height of the cup to C. This leaves enough room to connect 2 to 1 and 3, B to A and C. Then going under the handle, wrap around the cup to connect 1 to 3 and A to B. Now I patiently wait for the video to see if this is your solution :)
I don’t have any donuts handy to try this out on :o