#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!

This #spiral Fiddler from @xaqwg.bsky.social was fun and a lot more subtle than I expected. thefiddler.substack.com/p/can-you-ho... Might be a good distance investigation.

Fun #calculus fiddlers today from @xaqwg.bsky.social thefiddler.substack.com/p/can-you-to...

...strictly an overestimate, but within the bounds of my compute. joshmaxsilverman.github.io/2025-12-08-f... @xaqwg.bsky.social

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...

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...

Had to make some #geogebra for @xaqwg.bsky.social spirally Fiddler today. www.geogebra.org/m/k3a9s2ry thefiddler.substack.com/p/when-will-...

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 @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 I also got 12, but used different approach and also not very confident each cut is best... Tried a hybrid monte carlo approach to sample many different combinations of mow cuts and choosing the greediest for each one. colab.research.google.com/drive/1z6Cly...

#ThisWeeksFiddler @xaqwg.bsky.social Here is "a" solution to the extra credit. Very likely not "the" solution because I could only approximately calculate the volume remaining and couldn't figure out a way to find the greediest cylinder at each step. I obliterated the sphere in 12 steps. YMMV.

For @xaqwg.bsky.social 's #thisweeksfiddler, we're in a race where we increase our speed continuously to the end. (1+b)v(2x) = v(x), where x is the distance remaining in the race and b is the factor we increase our speed.

#ThisWeeksFiddler @xaqwg.bsky.social A 10-long river like this one happens only 405 times out of every 1,073,741,824.

in #thisweeksfiddler, we ask how long, on average, are coincidental diagonals of contiguous spaces in books written using 50% 3-letter, 50% 4-letter words with monospaced font.

My findings for #thisweeksfiddler by @xaqwg.bsky.social : How long is a river of spaces in a text? thefiddler.substack.com/p/how-long-i...

#ThisWeeksFiddler had a crystalline feel to it... but how many paths are there from the top to the bottom? Answer: Just over a billion. My solution: tinyurl.com/fiddler160525 @xaqwg.bsky.social

#ThisWeeksFiddler @xaqwg.bsky.social Extra credit: How many distinct paths are there from the top of a triangular bipyramid to the bottom, if (1) you never visit the same point twice and (2) you move only downward or sideways? Short answer: A lot, especially with larger bipyramids.

In #thisweeksfiddler we're asked to count the paths down a bipyramid, starting at the top and exiting the bottom, without taking any edge twice.

#ThisWeeksFiddler @xaqwg.bsky.social This chart shows how the likelihood of each series result depends on the probability p of the Celtics winning an individual game. The likelihood of "Celtics in 5" (blue line) is greater than the likelihood of any other result when p is between 0.6 and 0.75.

For #thisweeksfiddler by @xaqwg.bsky.social , we evaluate win probabilities for a best of 7 series. My graphical approach:

the standard credit is actually a bit more complicated, and is treated in the post. joshmaxsilverman.github.io/2025-05-04-f... @xaqwg.bsky.social

#ThisWeeksFidder @xaqwg.bsky.social The largest gaps seem to lie on either side of the nearest trees. The nearest tree is at (2,1) and it separates the 2 largest gaps. The next nearest trees are at (3,1), (3,2), (4,1), and (4,3). The illustration shows gaps when visibility is 100.

My findings for #Thisweeksfiddler, looking through the coprime forest. thefiddler.substack.com/p/can-you-se... @xaqwg.bsky.social

Classic coordinate puzzle from the Fiddler @xaqwg.bsky.social thefiddler.substack.com/p/can-you-se... first time I thought about this was in the CMP looking for Pythagoras (?) unit.

in #thisweeksfiddler we analyze the storied subgame of The Hammer in Tomorrow's Golf League. if a player throws the hammer, the opposing hammer has to accept it, doubling the value of winning the next hole, or reject it, automatically ceding 1 pt to the hammer thrower.

For #ThisWeeksFiddler: Another graph! @xaqwg.bsky.social

in #thisweeksfiddler we are looking for the smallest classroom size such that every possible group of k kids can approach the teacher for candy, and no consecutive two groups share a kid. to start, we look at the k=3 case, where trios of kids approach the teacher. @xaqwg.bsky.social

Can you solve #RegeneronSTS finalist Rivka Lipkovitz's favorite puzzle? @xaqwg.bsky.social open.substack.com/pub/thefiddl...

For #ThisWeeksFiddler by @xaqwg.bsky.social, March Mathness pt. 2 features rooting for the underdog! Full solution will be posted on Monday. #MarchMadness #Math

implementing the recursion, the probability for the 1-seed to win their region, seems to stabilize around ≈ 0.515431... for more details: https://joshmaxsilverman.github.io/2025-03-24-fiddler-ncaa-bracket/ @xaqwg.bsky.social

For #thisweeksfiddler by @xaqwg.bsky.social , how often will a 1-seed win a single elimination tournament, if in any matchup between teams with seeds M and N, the M-seed wins with probability N/(M+N)?

For #ThisWeeksFiddler by @xaqwg.bsky.social, we celebrate #MarchMadness with our very own March Mathness! 🏀 www.davidyding.com/navPages/rid...

In this week's Madness themed Fiddler, @xaqwg.bsky.social proposes this for seed win probability. I wonder about this every year! thefiddler.substack.com/p/can-you-pl... What's your head canon/model for this?

with the pdf in hand, we find the average distance to shore is 1/3-4/(9pi) ~= 0.19186. but we can better capture the plight of the everyman beachgoer with the median distance. binary searching the cdf, we find the 50th percentile beach distance is approximately 0.17426 @xaqwg.bsky.social

My findings for #Thisweeksfiddler by @xaqwg.bsky.social , where we try to escape pie, only to find pi. colab.research.google.com/drive/1ZTfQc...

#Thisweeksfiddler from @xaqwg.bsky.social asked: if you're randomly situated on a semicircular island, what is your expected distance from the coast? After a lot of geometry, calculus and algebra (plus a bit of help from WolframAlpha) I got a surprisingly simple answer. tinyurl.com/fiddler140325

For #ThisWeeksFiddler by @xaqwg.bsky.social, I wrote a special #PiDay #Math blog on finding the shortest distances to semi-circular beaches. www.davidyding.com/navPages/PiD...

For #ThisWeeksFiddler by @xaqwg.bsky.social, it's a Valentine's Day special for triangle lovers! 💘📐

in #thisweeksfiddler we want to fit hearts into small circles where the hearts are unit squares with unit diameter semi-circles fused on adjacent sides. for two, the most compact arrangement has radius 1.5, found by lining up two hearts along flat sides. @xaqwg.bsky.social

Actor makes political statement that actors should not make political statements. Fox News or The Onion? 😂

In 2024, the Yankees and Dodgers led the Majors in run differential. They combined to score 303 more runs than their opponents. Meanwhile, the White Sox were outscored by 306 runs, all on their own.

in #thisweeksfiddler we want to know: if we tumble the graph f(x,y) = |x| + |y|, what is the chance the new surface is a function? to deal with this, we have to turn the vertical line test into a condition. @xaqwg.bsky.social

For #ThisWeeksFiddler by @xaqwg.bsky.social, our frog friend isn't just happy sitting on lily pad #1, but rather on a natural log base! 🐸🌳 www.davidyding.com/navPages/rid...

This week's #Fiddler puzzle is a random walk: From (k), you hop to (k-1) with probability 1/k and hop to (k+1) otherwise. If you start at (2), what is the probability you eventually hop to (1)? @xaqwg.bsky.social I wrote a short tutorial here: laurentlessard.com/bookproofs/c...