#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 how the number of mulligans you have affects your expected score.

#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

A 10-long river like this one happens only 405 times out of every 1,073,741,824.

#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.