only if you work in $\mathbb Q[\sqrt 3]$. problem shown below is a hexagonal grid, or hexgrid. it’s similar to a square grid, but each cell of a hexgrid now has six neighbors. some cells are nu...

almost always. problem rob and bob are playing a game on an infinite binary tree. each edge of this tree has a probability $p$ of being colored red; otherwise it is blue. after both players hav...

usually, i come up with a good start, and iteratively refine it until i get a solution. not this time. problem fill a 5-by-5 grid with letters, one per cell. words can be spelled by making (che...

at least i found out what it can do. also, at least i finally refactored. problem the 11-by-11 grid below has been divided into various regions. shade some of the cells black, then place decima...

but only to check. problem $\DeclareMathOperator{\proj}{proj}\newcommand{\vctproj}[2][]{\proj_{#2}}\newcommand\dif{\mathop{}\mathrm{d}}$alice and bob play a game. at first, they start at the or...

i should definitely refactor. problem this grid can be partitioned into nine L-shaped “hooks”: the largest 9-by-9 (so, 17 squares total), then 8-by-8, all the way down to 1-by-1 (which is jus...

problem pick two points in a square, uniformly at random. what is the probability that the circle formed by taking the two points as a diameter is completely contained in the square? solution wo...

problem in the 2d plane, parallel lines are drawn 1 unit apart. drop a needle of length 1 onto this plane. what is the probability it crosses a line? source: buffon’s needle solution let the li...

that videogame helped me solve this. also i’m glad this puzzle was almost completely solvable by logic, with very little guesswork involved. problem shade a subset of the cells black such tha...

but, with the amount of recursive backtracking this thing has, it’d probably perform comparably in ocaml, with a lot less segfaults along the way. problem this grid can be partitioned into ni...