# Recreational Math Problems And Puzzles

## Articles, Results, and Questions

### Sokoban Maximum Moves

Which Sokoban boards have the longest shortest solutions for a fixed number of boxes and spaces?

### A350547: Equilateral Triangle-Free Hexagon Lattices

Let a(n) be the maximum size of a set of points taken from a hexagonal section of a hexagonal grid with side length n such that no three selected points form an equilateral triangle. What is a(n) for small values of n? How does a(n) grow as n increases?

### Maximum Sized Sets With Sums That Avoid Squares

{1, 6, 12, 14, 16, 17, 21, 23, 25, 27, 29, 31, 34, 36, 38, 40, 42, 44, 46, 49, 53, 55, 57}

Given a natural number n, what is the largest subset of the natural numbers up to n such that no sums of two elements from this subset are squares?

Here are a few puzzles located on the web that I enjoy (in no particular order):

Kattis: Lots of fun programming competition problems. This is my go-to site for programming competition practice.

Pathery: The goal is to be the first to find the best placement of walls to create longest path, and new puzzles are released at midnight everyday.

Robozzle: Difficult but fun robot programming puzzles. Tricky puzzles heavily favor recursive solutions.

Sokoban Online: The largest collection of classic and modern Sokoban puzzles that I've found, and the easiest interface to play them. I've published a few puzzles on this site.

Pathology: This is a another excellent collection of box-pushing puzzles with an active community. Optimal solutions are required to consider a level solved. I've published a few puzzles on this site.

Dr. Erich Friedman's Monthly Puzzle Site: A collection of packing, game theory, and graph theory related problems. I submitted results to this problem.

Al Zimmermann's Programming Contests: Very interesting NP Hard programming problems and competitions.

zachdestefano (at) gmail (dot) com