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I realised that even with the extra case for a double domino potentially using two squares in a set, I'd missed two tricks. Firstly, if the double domino is _required_ to use two of the squares, you can rule out any placement in which it only uses one. But I was only ruling out those in which it used _none_. Secondly, if you have the same number of squares as dominoes, so that the double domino _can_ but _need not_ use two of the squares, then I previously thought there was no deduction you could make at all. But there is! In that situation, the double does have to use _one_ of the squares, or else there would be only the n-1 heterogeneous dominoes to go round the n squares. So you can still rule out placements for the double which fail to overlap any square in the set, even if you can't (yet) do anything about the other dominoes involved.
This is the README accompanying the source code to Simon Tatham's puzzle collection. The collection's web site is at <https://www.chiark.greenend.org.uk/~sgtatham/puzzles/>. If you've obtained the source code by downloading a .tar.gz archive from the Puzzles web site, you should find several Makefiles in the source code. However, if you've checked the source code out from the Puzzles git repository, you won't find the Makefiles: they're automatically generated by `mkfiles.pl', so run that to create them. The Makefiles include: - `Makefile.am', together with the static `configure.ac', is intended as input to automake. Run `mkauto.sh' to turn these into a configure script and Makefile.in, after which you can then run `./configure' to create an actual Unix Makefile. - `Makefile.vc' should work under MS Visual C++ on Windows. Run 'nmake /f Makefile.vc' in a Visual Studio command prompt. - `Makefile.cyg' should work under Cygwin / MinGW. With appropriate tweaks and setting of TOOLPATH, it should work for both compiling on Windows and cross-compiling on Unix. - `Makefile.osx' should work under Mac OS X, provided the Xcode tools are installed. It builds a single monolithic OS X application capable of running any of the puzzles, or even more than one of them at a time. - `Makefile.wce' should work under MS eMbedded Visual C++ on Windows and the Pocket PC SDK; it builds Pocket PC binaries. Many of these Makefiles build a program called `nullgame' in addition to the actual game binaries. This program doesn't do anything; it's just a template for people to start from when adding a new game to the collection, and it's compiled every time to ensure that it _does_ compile and link successfully (because otherwise it wouldn't be much use as a template). Once it's built, you can run it if you really want to (but it's very boring), and then you should ignore it. DO NOT EDIT THE MAKEFILES DIRECTLY, if you plan to send any changes back to the maintainer. The makefiles are generated automatically by the Perl script `mkfiles.pl' from the file `Recipe' and the various .R files. If you need to change the makefiles as part of a patch, you should change Recipe, *.R, and/or mkfiles.pl. The manual is provided in Windows Help format for the Windows build; in text format for anyone who needs it; and in HTML for the Mac OS X application and for the web site. It is generated from a Halibut source file (puzzles.but), which is the preferred form for modification. To generate the manual in other formats, rebuild it, or learn about Halibut, visit the Halibut website at <https://www.chiark.greenend.org.uk/~sgtatham/halibut/>.