Zach Wissner-Gross

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

#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

Can You See Between the Trees? You are peering between trees positioned on an infinite grid. Where are the largest gaps between them that you can see?

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.