Gallimaufry of Games, 2000, updated in 2018
Playing the sum of several different combinatorial games can provide more understanding of each of them. In Winning Ways, Richard Guy coined the term "Gallimaufry" to refer to such a mixed sum.
In 2000, I composed a gallimaufry of positions in Domineering, Go, chess, and checkers. It was presented at the 4th Gathering for Gardner, known as G4G4. It was published in the Tribute volume by Rodgers and Wolfe under the deceptive title, "Four Games for Gardner". This title hid the fifth and most important problem, which was the gallimaufry, but its abbreviation fit the numerological strain of the gatherings. The sketched solution was published in "More Games of No Chance" under the title, "The 4G4G4G4G4 problems and solutions".
Unable to attend G4GXIII in 2018 in person, I submitted a video of this resurrected Gallimaufry, posted on this website as "Gallimaufry of Games". Here are the Powerpoint slides shown in that video.
Fibonacci Plays Billiards, Spring 2006, University of Calgary and August 6, 2016 in Columbus, OH
In 2006 the University of Calgary established an annual lecture in honor of Richard & Louise Guy. I gave this presentation (of which Richard Guy was the surprise co-author) as the first such lecture. Subsequent lecturers in this series are listed below.
A couple years earlier, we had driven together from Calgary to a game theory conference in Edmonton. When we stopped en route for lunch, we encountered a computer scientist at the next table who was heading to the same conference. He was engrossed in a problem which proved contagious. Richard and I joined in, and then veered off in our own direction. What follows is the Powerpoint of that talk. It includes some animated movies, of which Slide 65 is the most impressive.
On April 14th, 2007, a slightly refined version of this talk was given to a meeting of the Pacific Northwest section of the Mathematical Association of America, at Linfield College in McMinnville, OR, with Richard Guy in attendance again. And yet another version was given at the summer joint math meetings in Columbus OH on August 6, 2016, where it was the concluding talk of a special session celebrating Richard Guy's forthcoming 100th birthday on Sep 30, 2016. I discussed the talk privately with Richard the night before, and he told me that he had continued our study of the graph whose nodes are integers from 1 to N, where a branch joins two nodes iff their sum is a perfect square. This corresponds to the portion of the talk subtitled "Pythagoras Plays Billiards Too". Richard said that he had found explicit cycles in such graphs for every N running from the low 30s up to 250, although no pattern generalizable to arbitrary N had yet been found. So I announced that in my talk. He then presented his review/reaction/rebuttal, in which he revealed that following our discussion the night before, he had solved the case of N = 251.