>> Games without chance, welcome back. It's kind of wet here today, I hope you are having wonderful weather where you are. No, no, no cards today well. This is the quiz homework. So I'll, i'll, put up the quiz, and then we'll talk about a little bit directions for how to turn it in, and how to grade other quizzes and all that good stuff, is on the course website. So here's a question all about numbers. So in this quiz there are five questions. And the question, the answers are all about what numbers are these games. So the first game is this Hackenbush game with, that consists of, of, of this Hackenbush, this Hackenbush and this red 1 over here. So it's a sum of 3 Hackenbush positions. This is a number, what number is it? Two, three, and four, are games that are given in terms of, our notation for left options and right options. And game number five, here, is, is a sum of, of, of two such things. So, for this quiz, I'm expecting, for each one of these, a number as the answer. And they're usually relatively small numbers with relatively small denominators. I hope you all do well here and, ya'll come back now, you hear?