Centrist Groupoids Some of you will recall Central Groupoids, which are systems with a binary operator (magmas, shudder) that satisfy the equation AB.BC=B (or, (AB)(BC)=B), and have the curious property that the finite systems have a square number of elements. I decided to look at the relaxed equation AB.BA=B, which, after 30 seconds of deep thought, I have decided to call Centrist Groupoids. (Medial Magmas?) Of course, any Central Groupoid is also Centrist. The rule is anti-commutative. How Many of Order N? There are no 2- or 3-element systems. There are 58 4-element systems, and 6634 5-element systems, and no/nada/nil/0/zilch 6-element systems. Universal Equation Is there an equation that is true for all 2-element binary operators? (Besides A=A. :-)) PDP10 aficionados will recall the 16 boolean instructions (ANDCA, etc.). There are 10 non-isomorphic tables, or 7 if we allow argument swapping. (Zero, Left, And, Xor, Nor, ~Left, Andcm.) All of them satisfy the identity A:.A.AA:A = A:.AA.A:A or A{[A(AA)]A} = A{[(AA)A]A}. Puzzle: Show that similar equations exist with more letters, and for systems with more than 2 elements, and for ternary operators (tragmas). Problem: Find some. Somos Sequences etc. Gosper has come up with some interesting determinant identities for Somos sequences. I've finally updated my web page. Gosper's results, along with my foray into defining theta functions mod 43, are on the new page. I've also put up the slides from my Experimental Math talks, which include contributions from several Funsters. (counting polyhypercubes, ...) The page is at http://www.cs.arizona.edu/~rcs Rich rcs@cs.arizona.edu