Zach Wissner-Gross
@xaqwg.bsky.social
Math VP @Amplify. Co-Founder @SchoolYourself. Former Puzzle Editor @FiveThirtyEight. Opinions my own. he/him
thefiddler.substack.com
thefiddler.substack.com
Reposted by Zach Wissner-Gross
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...
www.davidyding.com/navPages/rid...
October 21, 2025 at 5:00 AM
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...
www.davidyding.com/navPages/rid...
Reposted by Zach Wissner-Gross
For #ThisWeeksFiddler by @xaqwg.bsky.social, I did some dice rolling, Monte-Carlo style:
www.davidyding.com/navPages/rid...
www.davidyding.com/navPages/rid...
Let’s Make a Tic-Tac-Deal!
Fiddler on the Proof: October 7, 2025
www.davidyding.com
October 14, 2025 at 5:46 AM
For #ThisWeeksFiddler by @xaqwg.bsky.social, I did some dice rolling, Monte-Carlo style:
www.davidyding.com/navPages/rid...
www.davidyding.com/navPages/rid...
Reposted by Zach Wissner-Gross
#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.
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.
October 7, 2025 at 12:23 PM
#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.
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.
Reposted by Zach Wissner-Gross
For #ThisWeeksFiddler by @xaqwg.bsky.social, I visualized an ant walking. 🐜🚶♂️
www.davidyding.com/navPages/rid...
www.davidyding.com/navPages/rid...
When Will You Cross Your Path?
Fiddler on the Proof: October 2, 2025
www.davidyding.com
October 6, 2025 at 4:42 AM
For #ThisWeeksFiddler by @xaqwg.bsky.social, I visualized an ant walking. 🐜🚶♂️
www.davidyding.com/navPages/rid...
www.davidyding.com/navPages/rid...
Reposted by Zach Wissner-Gross
Had to make some #geogebra for @xaqwg.bsky.social spirally Fiddler today. www.geogebra.org/m/k3a9s2ry
thefiddler.substack.com/p/when-will-...
thefiddler.substack.com/p/when-will-...
Ant Path Crossing
From a Fiddler problem.
www.geogebra.org
October 3, 2025 at 10:27 PM
Had to make some #geogebra for @xaqwg.bsky.social spirally Fiddler today. www.geogebra.org/m/k3a9s2ry
thefiddler.substack.com/p/when-will-...
thefiddler.substack.com/p/when-will-...
Reposted by Zach Wissner-Gross
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
www.davidyding.com/navPages/rid...
Also, check out my delicious take on the Basel Problem!
www.davidyding.com/navPages/Basel
@xaqwg.bsky.social
September 29, 2025 at 7:56 PM
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
www.davidyding.com/navPages/rid...
Also, check out my delicious take on the Basel Problem!
www.davidyding.com/navPages/Basel
@xaqwg.bsky.social
Reposted by Zach Wissner-Gross
#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.)
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.)
September 23, 2025 at 1:43 PM
#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.)
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.)
Reposted by Zach Wissner-Gross
#ThisWeeksFiddler @xaqwg.bsky.social
This chart shows how the number of mulligans you have affects your expected score.
This chart shows how the number of mulligans you have affects your expected score.
August 27, 2025 at 2:14 PM
#ThisWeeksFiddler @xaqwg.bsky.social
This chart shows how the number of mulligans you have affects your expected score.
This chart shows how the number of mulligans you have affects your expected score.
Reposted by 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.
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.
July 15, 2025 at 11:52 AM
#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.
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.
Reposted by Zach Wissner-Gross
For #thisweeksfiddler, what's the maximum score we can reach in bowling if we knock down a given number of pins? @xaqwg.bsky.social
July 15, 2025 at 2:24 AM
For #thisweeksfiddler, what's the maximum score we can reach in bowling if we knock down a given number of pins? @xaqwg.bsky.social
Reposted by Zach Wissner-Gross
#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.
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.
July 8, 2025 at 12:55 PM
#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.
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.
Reposted by Zach Wissner-Gross
#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...
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...
Google Colab
colab.research.google.com
June 24, 2025 at 3:08 PM
#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...
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...
Reposted by Zach Wissner-Gross
#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.
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.
June 24, 2025 at 1:55 PM
#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.
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.
Reposted by Zach Wissner-Gross
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.
June 16, 2025 at 5:41 PM
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.
Reposted by Zach Wissner-Gross
#ThisWeeksFiddler @xaqwg.bsky.social
A 10-long river like this one happens only 405 times out of every 1,073,741,824.
A 10-long river like this one happens only 405 times out of every 1,073,741,824.
May 27, 2025 at 1:41 PM
#ThisWeeksFiddler @xaqwg.bsky.social
A 10-long river like this one happens only 405 times out of every 1,073,741,824.
A 10-long river like this one happens only 405 times out of every 1,073,741,824.
Reposted by Zach Wissner-Gross
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.
May 26, 2025 at 8:52 PM
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.
Reposted by Zach Wissner-Gross
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...
May 26, 2025 at 5:29 PM
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...
Reposted by Zach Wissner-Gross
#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
My solution: tinyurl.com/fiddler160525
@xaqwg.bsky.social
May 19, 2025 at 7:06 PM
#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
My solution: tinyurl.com/fiddler160525
@xaqwg.bsky.social
Reposted by Zach Wissner-Gross
#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.
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.
May 19, 2025 at 5:25 PM
#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.
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.
Reposted by Zach Wissner-Gross
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.
May 19, 2025 at 2:22 PM
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.
Reposted by Zach Wissner-Gross
#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.
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.
May 12, 2025 at 8:07 PM
#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.
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.
Reposted by Zach Wissner-Gross
For #thisweeksfiddler by @xaqwg.bsky.social , we evaluate win probabilities for a best of 7 series. My graphical approach:
May 12, 2025 at 1:38 PM
For #thisweeksfiddler by @xaqwg.bsky.social , we evaluate win probabilities for a best of 7 series. My graphical approach:
Reposted by Zach Wissner-Gross
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
joshmaxsilverman.github.io/2025-05-04-f...
@xaqwg.bsky.social
May 5, 2025 at 12:31 PM
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
joshmaxsilverman.github.io/2025-05-04-f...
@xaqwg.bsky.social
Reposted by Zach Wissner-Gross
#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.
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.
April 29, 2025 at 11:29 AM
#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.
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.
Reposted by Zach Wissner-Gross
My findings for #Thisweeksfiddler, looking through the coprime forest. thefiddler.substack.com/p/can-you-se...
@xaqwg.bsky.social
@xaqwg.bsky.social
April 28, 2025 at 6:39 PM
My findings for #Thisweeksfiddler, looking through the coprime forest. thefiddler.substack.com/p/can-you-se...
@xaqwg.bsky.social
@xaqwg.bsky.social