A nice discussion of different proofs of the Hex Theorem: https://www.pureabstracts.com/blog/hex-cannot-end-in-a-draw

#CombinatorialGames

One of my students coded up some Toads and Frogs games last year and this semester wanted to improve the Elephants and Rhinos positions so they were all generated with mean value of zero.

The issue is that if you generate really random E&R boards, they are often either extremely unbalanced or there are very few moves available.

They got it working! Now you can play Elephants and Rhinos games where it's complicated to find and make the best moves. Try it out here:

https://kyleburke.info/DB/combGames/elephantsAndRhinos.html

(I don't want to say it's "hard" because you can still find them in polynomial time.)

#CombinatorialGames #UndergradResearch

#Sprouts2026 was yesterday and it was great! Sprouts is our annual conference in abstract games (often #CombinatorialGames) where students present #UndergradResearch for the contributed talks.

Here are my summaries of the talks: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-summaries.html

Here are a bunch of my after-the-fact thoughts: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-afterthoughts.html

I need to make sure I figure a bunch of those things out in time for next year!

Thank you to everyone who attended and especially to all of our great speakers. Craig and I agreed that we're very lucky to get such amazing talks!

The #Sprouts2026 program is coming along! We have nine contributed talks all lined up (from undergrads) and our keynote info should be going up later this week. https://kyleburke.info/sprouts/sprouts2026/

#CombinatorialGames #UndergradResearch

A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.

However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/

#maths #combinatorics #games #combinatorialgames

#ICCGTJ is already over! The last day of talks great! Here are my summaries: https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-four.html

Thanks to all the organizers and to everyone spreading #CombinatorialGames in Japan!

We had another great day of #ICCGTJ yesterday! Here are my quick talk summaries: https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-three.html

#CombinatorialGames

Day two of #ICCGTJ was excellent! We had multiple talks by teams of high schoolers, which is absolutely amazing. Here are my quick summaries: combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-two.html

#CombinatorialGames

Here are my summaries of the first day of talks at the International Conference on CGT in Japan (#ICCGTJ): https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-one-talks.html

Conference site: https://deguchikikaku.sakura.ne.jp/

#CombinatorialGames

Added another game to my playable list of games. (I implemented this year ago, then somehow lost it.) You can now play #Slimetrail: https://kyleburke.info/DB/combGames/slimetrail.html

#CombinatorialGames