TAOCP 7.2.2.1 Exercise 370

Section 7.2.2.1: Dancing Links

Exercise 370. ▶ [23] [23] Explain how to generate all of the $m \times n$ motley dissections that have 180°-rotational symmetry, as in the last two examples of exercise 365, by modifying the construction of exercise 366. (In other words, if $[a \ldots b) \times [c \ldots d)$ is a subrectangle of the dissection, its complement $[m - b \ldots m - a) \times [n - d \ldots n - c)$ must also be one of the subrectangles, possibly the same one.) How many such dissections have size $8 \times 16$?

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