by **tso** » Tue Nov 22, 2005 5:50 pm

In this case, the naked quad and the hidden triple are two names for exactly the same deduction. Which is simpler to spot is subjective. This illustrates a specific case of a broader point -- that the "next logical step" is ususally subjective. An xy-wing is by consensus more advanced or more difficult to find than a naked pair -- but if you see one while there are still naked pairs available, well, then that's your next logical step. Personally, I often find it much easier to spot even longer forcing chains than uncovering naked quads or hidden anythings, as I can focus only on bi-value cells.

In this case, I might have missed the naked quad and instead found a simple xy-type forcing chain:

r6c3=5 => r2c3=6

r6c3=9 => r9c3=3 => r9c7=9 => r8c8=6 => r2c8=5 => r2c3=6

Therefore, r2c3=6 and the rest is easy.

Who's to say that this isn't just as valid of a "next logical step" as the naked quad/hidden trip?

To some degree, how difficult a specific tactic is perceived is changed by what point you typically attempt to apply it. If you always wait until your bag of tricks is empty to try a specific tactic, you might rate it as the most advanced or difficult tactic while another solver might find that same tactic more of a standard tool to check for earlier on. I have solved many puzzles that supposedly required some combination of x-wings, swordfish, coloring, quads and such, only to find that a single xy-wing, forcing chain or uniqueness brought me to the solution quicker, skipping over all of the "required" tactics. If you find a naked pair, you might as well see if you can make a uniqueness elimination. If you're looking for naked triples, you might as well check for xy-wings at the same time.

The x-wing that CathyW spotted isn't needed as there is a hidden single at r8c8 that accomplishes the same eliminations -- but which is more fun to find? Did CathyW make a mistake by missing the simpler elimination? I don't think so. We are not just rats in the maze following the one and only path to the cheese.