Tom Keith
@tomkeith.bsky.social
#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. #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.) #ThisWeeksFiddler @xaqwg.bsky.social:
This chart shows the probability of being able to achieve various dollar amounts of cash if you start with three $10 vouchers and one $25 voucher and play optimally for each amount. #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. #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. #ThisWeeksFiddler @xaqwg.bsky.social
EEC: There is a faint message scrawled onto the second scroll which you can barely make out: "Nullus numerus repetitur", i.e., "No number is repeated".
How many combinations are possible if none of the eight numerical inputs is used more than once? #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. #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. #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. #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. #ThisWeeksFiddler 28 Mar 2025
I tried running the tournament with different boost values, namely 0.5, 1.5, 2.5, and 3.5.
Every team won except for the team with power index 3. 
