TAOCP 7.2.2.1 Exercise 302

Section 7.2.2.1: Dancing Links

Exercise 302. [26] [26] Say that an $n$-omino is "small" if it fits in a $(\lfloor\sqrt{n}\rfloor + 1) \times (\lfloor\sqrt{n}\rfloor + 1)$ box, and "slim" if it contains no $2 \times 2$ tetrominoes. Thus, for example, pentominoes Q, S, Y aren't small; P isn't slim.

a) How many small-and-slim $n$-ominoes are both small and slim? b) Fit nine different small-and-slim nonominoes into a $9 \times 9$ box. c) Use a solution to (b) as the basis of a jigsaw sudoku puzzle with a unique solution. The clues of your puzzle should be the initial digits of $\pi$.

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