A Sudoku question for the experts: Suppose I generate a random Sudoku puzzle: Select a completed sudoku at random from the gazillion or so distinct sudokus. Then delete entries at random, stopping when nothing further can be removed without making the problem ambiguous. [This is a poor man's substitute for selecting a truly random minimal puzzle, which I suspect is much harder to do.] How hard, on average, is the resulting Sudoku? Are there very difficult Sudokus? Everything I've seen can be solved with at worst "single guessing", where a branch is tried and one of the possibilities leads to a quick contradiction without sub-guessing, or both branches lead to a same-forced- value. I.e., if the correct "cell to branch on" is selected, one of the branches dies and no recursion is necessary. ---- A challenge for numerical topology: Most materials -- cloth, paper, tape, plastic sheet, wood, metal, can stretch or shrink a bit in order to fit together. Even glass is slightly flexible. People who work with these materials for a living -- tailors, carpenters, ... -- have an intuitive feeling for how much their medium can stretch, bend, or twist, and what manipulations are required to make the pieces fit. Here's the challenge: Come up with a theory of making things fit -- a theory of wrinkles, shims, pleats, and all the other myriad tricks, fiddles, and adjustments that the subject experts know. Rich