#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!

All I see is blonde, brunette, redhead…

Can You Hop in a Spiral? A frog hops around a pond packed with lily pads, spiraling slightly outward with each jump. What’s the tightest spiral it can make?

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.

Can You Topple the Tower? You’re building a block tower with an overhang. How long must this overhang be for the tower to come tumbling down?

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

Can you fling the fractal darts? How many points will you asymptotically approach?

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

Stay tuned!

Correct!

I use GPT5-Reasoning, so we shall see!

Welcome back!!

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...

Let’s Make a Tic-Tac-Deal! Fiddler on the Proof: October 7, 2025

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.

When Will You Cross Your Path? Fiddler on the Proof: October 2, 2025

For #ThisWeeksFiddler by @xaqwg.bsky.social, I visualized an ant walking. 🐜🚶‍♂️

www.davidyding.com/navPages/rid...

Ant Path Crossing From a Fiddler problem.

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

Welcome back, David!!!

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.)

“Survival” definitely not the right word here. 🙃

Survival of the nitwittest.

#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.

Google Colab

#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...

A lattice of 30 points arranged in a trigonal bipyramid

#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