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 Post subject: Rotational Symmetry
PostPosted: Fri Jun 05, 2009 10:41 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
This can be considered either as a technique or an interesting shortcut.

It comes from A123 "Roulette" here.

Image

This works when all cages are symmetrical about the centre cell R5C5, as in the diagram, and their totals are complementary. In this example all pairs of 3-cell cages that are symmetrical about the centre must have a combined total of 30, for example R1C456 = 6 and R9C456 = 24 total 30, and all pairs of 6-cell cages such as the ones in N1 and N9 must have a combined total of 60. The puzzle must also have a unique solution, which of course applies for all puzzles posted on this site.

udosuk provided an excellent graphical explanation of why this works here. The result is that R5C5 is a complementary cage with itself and therefore R5C5 = 5.

This and the harder A123 V2 are the only puzzles I've seen, so far, where this technique can be used.


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