Zach Wissner-Gross

#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.

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 a High Schooler’s Favorite Puzzle? Rivka Lipkovitz has excelled in mathematics research competitions. Do you have what it takes to solve one of her favorite math puzzles?

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

Correct! I have updated the puzzle to specify there are at least 4 students in the class.

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)?

Can You Play the Favorite? Fiddler on the Proof: March 21, 2025

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...