#ThisWeeksFiddler by @xaqwg.bsky.social put a rover on a spherical planet with radius 1000 miles, and drove it three straight segments of the same length with 60 degree turns in between, arriving back at its starting point.
The maths was the easy bit... the animation took far too much of my time!
@xaqwg.bsky.social in my original submission to #thisweeksfiddler, i coded up the recursion eqn and forgot about it. this morning at the vet, i realized it's a nice extension of the basic random walk. the probability distribution is made up of a sum of static patterns on the lattice.
In #thisweeksfiddler we mix coffee and tea. Why ruin good tea? I dunno, but I'm on board with ending up with as little coffee as possible. docs.google.com/document/d/1...
#thisweeksfiddler
I hit on the below 6x6 prime magic square but unable to find an 8x8. Interested if anyone hit on an 8x8 or larger one...
337 367 307 421 241 353
293 331 383 271 317 431
389 281 347 359 439 211
401 167 313 349 647 149
233 311 17 487 379 599
373 569 659 139 3 283
in #thisweeksfiddler we descend all levels of the apollonian dartboard, receiving a multiplier bonus on our throw from the dartboard's fractal structure. recursion by hand and by my computer gives a 100M+ circle estimate of 3.71086...
For #thisweeksfiddler by @xaqwg.bsky.social , we find the probability that you win a best-of-N series, given that you win vs. lose the very first game.
For #ThisWeeksFiddler by @xaqwg.bsky.social, check out my write-up and animation as my best attempt to explain why direction picking doesn't always equate to angle picking, especially when things go 3D.
www.davidyding.com/navPages/rid...
#thisweeksfiddler kinda looks like a Mercator projection, if you squint. drive.google.com/file/d/1m90j...
For #ThisWeeksFiddler by @xaqwg.bsky.social, I did some dice rolling, Monte-Carlo style:
www.davidyding.com/navPages/rid...
#ThisWeeksFiddler @xaqwg.bsky.social: Anita the Ant
To figure out what was going on, I made an animation. I found that Anita the Ant's path ended up inscribing a 2-3-2 isosceles triangle.
For #ThisWeeksFiddler by @xaqwg.bsky.social, I visualized an ant walking. 🐜🚶♂️
www.davidyding.com/navPages/rid...
I'm back to solving #ThisWeeksFiddler after taking a break to deal with some personal matters! For this week, I am taking a few risks:
www.davidyding.com/navPages/rid...
Also, check out my delicious take on the Basel Problem!
www.davidyding.com/navPages/Basel
@xaqwg.bsky.social
#ThisWeeksFiddler @xaqwg.bsky.social
Here are the average lengths of the longest increasing subsequences of all the permutations of n elements.
(The numerators in the table come from oeis.org/A003316.)
#ThisWeeksFiddler @xaqwg.bsky.social
This chart shows how the number of mulligans you have affects your expected score.
#thisweeksfiddler
Miles Probability
3 17/256
3.5 32/256
4 24.75/256
4.5 72/256
5 9.1875/256
5.5 33/256
6 20.0625/256
6.5 48/256
Avg = 3*17/256+3.5*32/256+4*(24+3/4)/256+4.5*72/256+5*(9+3/16)/256+5.5*33/256+6*(20+1/16)/256+6.5*48/256
= 19933/4096 ~ 4.8665 miles
For #thisweeksfiddler, we race among randomly selected loops of length 1, 3, 3.5, 4.5 miles at a 10 min/mi pace. If unfinished loops don't count and we have 65 min left to race, how can we maximize the avg total distance completed?
For #thisweeksfiddler by @xaqwg.bsky.social , we start with a set of vouchers ($10, $10, $10, $25), and can bet any of them on either side of an even odds game.
Chart showing (dollar amount, probability): ($30, 100%), ($35, 100%), ($40, 87.5%), ($45, 81.641%), ($50, 76.562%), ($55, 68.75%), ($60, 68.75%), ($65, 59.375%), ($70, 59.375%), ($75, 50.781%), ($80, 50.195%), ($85, 50%), ($90, 50%), ($95, 43.75%), ($100, 40.82%), ($105, 38.281%), ($110, 34.375%), ($115, 34.375%), ($120, 29.688%), ($125, 29.688%), ($130, 25.391%), ($135, 25.098%), ($140, 25%), ($145, 25%), ($150, 21.875%)
#ThisWeeksFiddler @xaqwg.bsky.social:
This chart shows the probability of being able to achieve various dollar amounts of cash if you start with three $10 vouchers and one $25 voucher and play optimally for each amount.
#ThisWeeksFiddler
EC: W= $90 cash with 50% likelihood from the outset.
First bet the entire $55 on one side. This has 50% probability of winning $55 cash while retaining the $55 of vouchers.
After winning use the same strategy as in Part 1 to add $35 or more cash guaranteed.
For #thisweeksfiddler, we're blocking our friend from placing their square on a board of side length B using 3 of our own.
#ThisWeeksFiddler
I got an answer for both the _A_ and _B_ but I'm not really happy with how I arrived at each of them
here is an animation for A
thefiddler.substack.com/p/can-you-sq...
In #thisweeksfiddler, it's a sprint to the finish of the Tour de France ... isn't it? drive.google.com/file/d/11VEt...
#thisweeksfiddler @xaqwg.bsky.social
Other bikers will sprint if their strength >0.5, while we sprint if our leg strength >t. What is our chance of winning?
in #thisweeksfiddler we are asked to find the expected maximum number of friends who are at the mall at the same time, given that they all go at a random 15 min window over an hour. i wondered about the large N behavior.
#ThisWeeksFiddler @xaqwg.bsky.social
I wrote code to emulate playing the game of bowling. I found 420,571 possible states in the game including 25,646 terminal states.
With this list in hand, it was a matter of finding the terminal states that best qualified in each case.
For #thisweeksfiddler, what's the maximum score we can reach in bowling if we knock down a given number of pins? @xaqwg.bsky.social
#ThisWeeksFiddler @xaqwg.bsky.social
How many different equilateral triangles in the game of Dozo?
I found 11 different sizes of triangle. The smallest appeared at 36 different locations and orientations on the Dozo board. The largest appeared just once.
#ThisWeeksFiddler @xaqwg.bsky.social
EEC: There is a faint message scrawled onto the second scroll which you can barely make out: "Nullus numerus repetitur", i.e., "No number is repeated".
How many combinations are possible if none of the eight numerical inputs is used more than once?
