What is this ColorTaiko! game?

The ColorTaiko! project will not run under IML formally in Fall 2025, but we do want to keep improving the game. If you are a student at UIUC and want to join this project in Fall 2025, talk to me in person soon (say, by coming to my 490 class.) Depending on the number of volunteers, we will need to see how to formally arrange this. (Say, as part of my informal IG³OR'S group, or maybe by registering to a course with me.)
Experience: JavaScript will be needed. General experience with algorithms, game design, web design and React is helpful. Weekly commitment is expected from participants.

The idea of this game originated from Igor Mineyev's article The topology and geometry of units and zero-divisors: origami. The article describes how certain colorings of bipartite graphs (if found) lead to counterexamples to Kaplansky conjectures - important problems in algebra. So if you can play the (coming) harder versions of the game till the end (bringing the success to 100%), then you will automatically produce a counterexample for this important math problem.

This project ran as an IML project in the Mathematics Department, UIUC, in Spring 2024, and it continues in Fall 2024. Feel free to play the currently-available, preliminary, kindergarten-level version of the game. This is level 1. We plan to continue improving the game in the foreseeable future, and also to add levels 2, 3, etc, so come again and play again.

Thanks to the University of Illinois Campus Research Board for providing support for hosting this game on the UIUC domain, made possible by award RB22075 to Igor Mineyev in March 2022.

Igor Mineyev's grant application to the Topology program at the National Science Foundation (NSF) in Fall 2023 asking for support for this game, for the research it is based on, and for the people involved in the project, was expressly NOT supported by NSF. This preliminary version of the game that you see here was created by our heroic efforts in spite of NSF's refusal to support that proposal.

More information will appear here as we proceed.

To learn how to play the game, just play it! If you would like to see a formal description of the rules, here they are: rules for level 1, rules for level 2, rules for level 3.

THE HALL OF FAME: THE HONORED PARTICIPANTS AND CREATORS IN THIS PROJECT.

In Fall 2025 (independent project, part of IG³OR'S group):
Professor: Igor Mineyev.
Graduate mentor: Jihong Cai.
Undergraduate students: Haozhe Li, Wenchang Qi, Prithiv Sudhakar.

In Spring 2025 (as an IML project):
Professor: Igor Mineyev.
Graduate mentor: Jihong Cai.
Undergraduate students: Arjun Chatterjee, Matthew Guerra, Christopher Monzon, Wenchang Qi, Nick Wong, Linda Yan, Yixu Zheng.

In Fall 2024 (as an IML project):
Professor: Igor Mineyev.
Graduate mentors: Jihong Cai, Zishen Qu.
Undergraduate students: Maxwell Liu, Shrut Patel, Ila Petrovic, Wenchang Qi.

In Spring 2024 (as an IML project):
Professor: Igor Mineyev.
Graduate mentors: Aziz Bouland, Manisha Garg.
Undergraduate students: Enson Gai, Aditya Kshirsagar, Kevin Liu, Anvitha Manepalli, Jeongjae Park, Aditya Ved.

The link to this and other games is available from Igor Mineyev's Math Page.