Mentor: Anna Schilling 

Team members: Victoria Weidmann (Graf-Eberhard-Gymnasium Bad Urach)

Description: This week it was all about the Rubik's Cube, which can be beautifully described using group theory. To do this, we first looked at groups in general and then specifically at the symmetric group $S_n$. We also had to figure out how to uniquely describe a cube mathematically. We were then able to devote ourselves to the proof of the “solvability theorem”, which clearly characterizes how you can tell from a twisted cube whether it is solvable.
For the game SET, we looked at the mathematical description and how many cards there can be without a set.

Mentor: Anna Schilling

Team members: Sophie Rehberger (Englisches Institut Heidelberg), Sophie Rupp (Englisches Institut Heidelberg)

Description: During the one week of internship, we worked on the games “Dobble” and “SET” and analyzed their structures. We learned about projective geometry, which is closely linked to the game Dobble, and created our own game. We learned how the game SET can be described mathematically and we found out the maximum number of cards there can be without a set.

Mentors: Anna Schilling, Diaaeldin Taha
Team members: Paul Martin
Description: In this two-week internship, we learned about the mathematics of random walks in the hyperbolic plane and simulated these dynamical systems.
Online app: link

Mentors: Anna Schilling, Diaaeldin Taha
Team members: Max Dörich (DBG Eppelheim), Lukas Kühlwein (DBG Eppelheim)
Details: This project aimed to introduce the interns to the mathematics of games of chance and skill using computer explorations. During the first week, we studied the game SET using algebra, geometry, combinatorics, and computer simulations. During the second week, we learned about the Sprague–Grundy theorem, and how to write programs that play famous impartial games perfectly.
GitHub: link