given the three kinds of puzzle pieces pictured on the left, define a puzzle to be a decomposition of a triangle into puzzle pieces (such that the edges match up, like in a jigsaw puzzle). call a puzzle ``rigid'' if there is no other puzzle with the same outer boundary. a lot can be proven about puzzles (we'll do (1) and (2) in the talk): \vskip .05in \noindent 1. the number of $0$s on one side equals the number of $0$s on each of the other two sides - see if you can prove this one before the talk! \vskip .05in \noindent 2. the lines in the puzzle pieces can all be simultaneously straightened (as in the right-hand picture) if and only if the puzzle is rigid. \vskip .05in \noindent 3. there is an easy 1:1 correspondence between rigid puzzles and inequalities on the eigenvalues of the sum of two hermitian matrices. \vskip .05in \noindent 4. the statement ``given four generic lines in space, there are exactly two others that touch all four,'' and others like it, can be turned into puzzle-counting statements. \vskip .1in \noindent refreshments will be provided!