math them

Today we'll look at some explorations based on the chip-firing game.

Today we'll look at an activity based on covering the integers with arithmetic sequences.

I'm in New Jersey this week, so thought I'd break format and give an update on a couple of topics that connect to the trip!

My colleague Asmita Sodhi has been presenting some of the mathematics of the game Spot It! in the problem incubator this week and last, which reminded me of an activity I've run before, charging students with designing their own Spot It!-like game. Today we'll look at an iteration of that, using Asmita's "Double Spot It!" for an added challenge.

It's tough coming up with a good activity that deals with numbers or geometry in a continuous way, since it usually requires a good amount of prerequisite knowledge. Today's activity is a set of discrete puzzles inspired by a continuous result colloquially known as the ham sandwich theorem.

My colleague Daniel Kline has been playing around with a novel set of puzzles to be solved with a Soma cube that should hopefully hit the website in coming months. I wanted to create something that was less reliant on gravity and friction and ended up with a slightly more traditional puzzle set.

A nice source of generalizations for classic games played on a tabletop is porting them over to other surfaces. Today we'll look at Tic Tac Toe on more exotic surfaces than the standard \(3 \times 3\) board.

In order to spice up classical combinatorial games, mathematicians have explored what happens if, instead of alternating turns, players bid each turn for the opportunity to make a move. Here we'll look at Tic Tac Toe with such a bidding scheme.