@xaqwg.bsky.social in my original submission to #thisweeksfiddler, i coded up the recursion eqn and forgot about it. this morning at the vet, i realized it's a nice extension of the basic random walk. the probability distribution is made up of a sum of static patterns on the lattice.

in #thisweeksfiddler we descend all levels of the apollonian dartboard, receiving a multiplier bonus on our throw from the dartboard's fractal structure. recursion by hand and by my computer gives a 100M+ circle estimate of 3.71086...

in #thisweeksfiddler we are asked to find the expected maximum number of friends who are at the mall at the same time, given that they all go at a random 15 min window over an hour. i wondered about the large N behavior.

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.

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.

in #thisweeksfiddler the question is, on average, how many rides will be taken by holders of the lightning pass, assuming their initial rides are assigned at random from the days hourly time slots and they can hold three reservations at any given time?

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.

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

in #thisweeksfiddler, we want to know the chance that a 1-seed makes the final four, given that (2^d-1) inferior teams stand in their way.

in #thisweeksfiddler, we're kidnapped and wake up in a stupor at some random position on a semi-circular island. what is our distance to the nearest shore, probably? joshmaxsilverman.github.io/2025-03-16-f...

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

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