A mathematically minded programmer writes about probability, puzzles, geometry and everyday calculations, such as Skittles duplicates and using a watch as a compass.
HN commenters link it for its Skittles birthday paradox analysis, watch compass trick and blackjack posts, and the author joins the discussion himself.
You could probably make it in a few minutes - the direction of the sun is, to a first approximation, 15 degrees times the number of hours it is after midnight. This leads to a trick for using an analog watch as a compass:
https://www.citizenwatch-global.com/support/exterior/direction.html
https://www.watchaffinity.co.uk/blog/how-to-use-your-watch-as-a-compass/
This is more prone to errors closer to the equator and in the summer (https://possiblywrong.wordpress.com/2012/01/25/using-a-watch-as-a-compass/) but should be good enough for picking a side of the bus.
(This is all in the northern hemisphere; in the southern hemisphere the sun goes the other way, so change the sign on everything.)
0.1mm is not very smooth. According to wikipedia, 150 grit sandpaper has average particle size of 90-100µm
edit: of course there is vigorous internet commentary about billiard ball smoothness compared to earth:
https://possiblywrong.wordpress.com/2011/01/03/is-the-earth-like-a-billiard-ball-or-not/
https://skeptics.stackexchange.com/questions/10763/is-earth-as-smooth-as-a-billiard-ball
https://billiards.colostate.edu/faq/ball/smooth/
Which mostly seem to agree that earth definitely is not as smooth as a (new) billiards ball, but there is lots of debate about the details.
I'm pretty sure there is some fundamental queueing theory to back this up, as it's the main takeaway I had from a queuing theory course I took in college. Can't remember the details though, so I'm not sure it would still apply if a single queue entailed long walks from the head of the queue to the nearest available 'processor'.
EDIT: more background here
https://possiblywrong.wordpress.com/2010/12/26/why-multiple-checkout-lines-are-not-all-bad/
It appears you might be right in practice.
The picture he shows of all the Skittles' counts looks like something I would've seen at the local museum. He missed his chance of taking an ultra high resolution photo of it and putting it on display:
https://possiblywrong.wordpress.com/2019/04/06/follow-up-i-found-two-identical-packs-of-skittles-among-468-packs-with-a-total-of-27740-skittles/#jp-carousel-3199
In a similar vein, I saw this linked from HN not too long ago and thought it was a really neat application of the birthday paradox--all about finding duplicate packs of Skittles: https://possiblywrong.wordpress.com/2019/04/06/follow-up-i-found-two-identical-packs-of-skittles-among-468-packs-with-a-total-of-27740-skittles/
Why? There are very efficient machine-learning-free solutions... There are even rote solutions a human can use n his own head with a bit of practice. The game is basically solved.
https://possiblywrong.wordpress.com/?s=blackjack