Sign in

Zach Wissner-Gross

@xaqwg.bsky.social
160 followers 35 following 27 posts

Math VP @Amplify. Co-Founder @SchoolYourself. Former Puzzle Editor @FiveThirtyEight. Opinions my own. he/him thefiddler.substack.com

PostsRepliesMedia
Reposted by Zach Wissner-Gross
Mike Porter @profmikeporter.bsky.social · 16/02/2026
#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!
021
Reposted by Zach Wissner-Gross
John Golden @johngolden.bsky.social · 31/01/2026
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.
thefiddler.substack.com
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?
061
Reposted by Zach Wissner-Gross
John Golden @johngolden.bsky.social · 12/12/2025
Fun #calculus fiddlers today from @xaqwg.bsky.social thefiddler.substack.com/p/can-you-to...
thefiddler.substack.com
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?
041
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 08/12/2025
...strictly an overestimate, but within the bounds of my compute. joshmaxsilverman.github.io/2025-12-08-f... @xaqwg.bsky.social
joshmaxsilverman.github.io
Can you fling the fractal darts?
How many points will you asymptotically approach?
121
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 21/10/2025
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...
031
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 14/10/2025
For #ThisWeeksFiddler by @xaqwg.bsky.social, I did some dice rolling, Monte-Carlo style: www.davidyding.com/navPages/rid...
davidyding.com
Let’s Make a Tic-Tac-Deal!
Fiddler on the Proof: October 7, 2025
131
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 07/10/2025
#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.
021
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 06/10/2025
For #ThisWeeksFiddler by @xaqwg.bsky.social, I visualized an ant walking. 🐜🚶‍♂️ www.davidyding.com/navPages/rid...
davidyding.com
When Will You Cross Your Path?
Fiddler on the Proof: October 2, 2025
141
Reposted by Zach Wissner-Gross
John Golden @johngolden.bsky.social · 03/10/2025
Had to make some #geogebra for @xaqwg.bsky.social spirally Fiddler today. www.geogebra.org/m/k3a9s2ry thefiddler.substack.com/p/when-will-...
geogebra.org
Ant Path Crossing
From a Fiddler problem.
041
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 29/09/2025
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
131
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 23/09/2025
#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.)
121
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 27/08/2025
#ThisWeeksFiddler @xaqwg.bsky.social This chart shows how the number of mulligans you have affects your expected score.
031
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 15/07/2025
#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.
221
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 15/07/2025
For #thisweeksfiddler, what's the maximum score we can reach in bowling if we knock down a given number of pins? @xaqwg.bsky.social
021
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 08/07/2025
#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.
121
Reposted by Zach Wissner-Gross
Jason Weisman @jlw12.bsky.social · 24/06/2025
#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...
colab.research.google.com
Google Colab
131
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 24/06/2025
#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.
221
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 16/06/2025
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.
111
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 27/05/2025
#ThisWeeksFiddler @xaqwg.bsky.social A 10-long river like this one happens only 405 times out of every 1,073,741,824.
041
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 26/05/2025
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.
151
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 26/05/2025
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...
041
Reposted by Zach Wissner-Gross
Mike Porter @profmikeporter.bsky.social · 19/05/2025
#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
A lattice of 30 points arranged in a trigonal bipyramid
051
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 19/05/2025
#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.
261
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 19/05/2025
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.
151
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 12/05/2025
#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.
141
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 12/05/2025
For #thisweeksfiddler by @xaqwg.bsky.social , we evaluate win probabilities for a best of 7 series. My graphical approach:
031
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 05/05/2025
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
121
Reposted by Zach Wissner-Gross
Tom Keith @tomkeith.bsky.social · 29/04/2025
#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.
131
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 28/04/2025
My findings for #Thisweeksfiddler, looking through the coprime forest. thefiddler.substack.com/p/can-you-se... @xaqwg.bsky.social
031
Reposted by Zach Wissner-Gross
John Golden @johngolden.bsky.social · 26/04/2025
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.
thefiddler.substack.com
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?
031
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 21/04/2025
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.
241
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 14/04/2025
For #ThisWeeksFiddler: Another graph! @xaqwg.bsky.social
041
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 07/04/2025
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
261
Reposted by Zach Wissner-Gross
Society for Science @society4science.bsky.social · 04/04/2025
Can you solve #RegeneronSTS finalist Rivka Lipkovitz's favorite puzzle? @xaqwg.bsky.social open.substack.com/pub/thefiddl...
open.substack.com
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?
011
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 30/03/2025
For #ThisWeeksFiddler by @xaqwg.bsky.social, March Mathness pt. 2 features rooting for the underdog! Full solution will be posted on Monday. #MarchMadness #Math
131
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 25/03/2025
implementing the recursion, the probability for the 1-seed to win their region, seems to stabilize around ≈ 0.515431... for more details: joshmaxsilverman.github.io/2025-03-… @xaqwg.bsky.social
041
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 25/03/2025
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)?
051
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 24/03/2025
For #ThisWeeksFiddler by @xaqwg.bsky.social, we celebrate #MarchMadness with our very own March Mathness! 🏀 www.davidyding.com/navPages/rid...
davidyding.com
Can You Play the Favorite?
Fiddler on the Proof: March 21, 2025
061
Reposted by Zach Wissner-Gross
John Golden @johngolden.bsky.social · 21/03/2025
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?
021
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 18/03/2025
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
011
Reposted by Zach Wissner-Gross
spottedgeck.bsky.social @spottedgeck.bsky.social · 18/03/2025
My findings for #Thisweeksfiddler by @xaqwg.bsky.social , where we try to escape pie, only to find pi. colab.research.google.com/drive/1ZTfQc...
221
Reposted by Zach Wissner-Gross
Mike Porter @profmikeporter.bsky.social · 17/03/2025
#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
072
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 17/03/2025
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...
341
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 16/02/2025
For #ThisWeeksFiddler by @xaqwg.bsky.social, it's a Valentine's Day special for triangle lovers! 💘📐
davidyding.com
Can You Squeeze the Heart? (Valentine's 2025 Special)
Fiddler On The Proof: February 14, 2025
141
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 17/02/2025
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
151
Zach Wissner-Gross @xaqwg.bsky.social · 16/02/2025
Actor makes political statement that actors should not make political statements. Fox News or The Onion? 😂
110
Zach Wissner-Gross @xaqwg.bsky.social · 15/02/2025
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.
020
Reposted by Zach Wissner-Gross
joshmaxsilverman.bsky.social @joshmaxsilverman.bsky.social · 03/02/2025
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
151
Reposted by Zach Wissner-Gross
David Ding @david-ding.bsky.social · 27/01/2025
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...
051
Reposted by Zach Wissner-Gross
Laurent Lessard @laurentlessard.bsky.social · 26/01/2025
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...
laurentlessard.com
Can you hop to the lily pad? - Book Proofs
This week's Fiddler is about hopping back and forth. You are a frog in a pond with an infinite number of lily pads in a line, marked "1," "2," "3," etc. You are currently on pad 2, and your goal is to...
051