Tristan Miller is developing a combinatorics game that will generate combinatorics problems and provide graphical and algebraic tools to solve them. Examples include finding permutations of ice cream flavors or determining the most likely distribution of balls in an urn based on random draws. The game aims to first teach counting techniques in probability and then apply those skills to make inferences about unknown scenarios.

1. Software developments by Tristan Miller
Combinatorics Game
This will essentially be a generator of combinatorics problems.
A graphical interface will provide various means of solving a problem – by finding and counting
permutations, using structures such as tree diagrams to do this more efficiently, or by using
algebraic tools.
An example: how many ways can three ice-cream flavours be arranged?
The interface would allow the player to visually arrange the flavours to find every possible
permutation. Alternatively, they could apply mathematical theory to sort it out.
This could be expanded into exploring various interesting probability problems, including Bayesian
inference.
The following kind of modelling problem could be readily implemented:
An urn contains eight balls, some are red, the rest are white.
Drawing three balls at random without replacement, you obtain two reds and one white.
What is the most likely assortment of balls?
Thus the idea of the program is to first build familiarity with counting techniques in probability, then
apply these ideas to make inferences about unknown situations.