Puzzle Description Suppressed:Click below to view spoilers

#1: Tom O'Connell (sensei69) on Mar 15, 2011

hi bak @ ya

interesting logic on the mouth

You have two ways of looking at this - either a mega-smile, or as zig-zag logic. Either way is deep lookahead.


The zig-zag logic is more "logical" than the mega-smile.

The mega-smile depends on you recognizing a smile-like pattern to the clues, and then placing them to see if it works. However, since you're starting from an assumption, just because it works doesn't mean that there isn't another way that will also.

For zig-zag logic, you must realize that all those crossing 2s mean either a bunch of 2x2 blocks or zig-zags. with the 1s the probability tilts toward zig-zags.

To prove this, we must check each starting point for a zig-zag (the possible 1 positions in r12). If the left one is in c5 then it extends into r13, which then extends into c6, which then extends into r14... etc. That one works, but since we started by assumption, we just leave it blank since all we have proven is that it *could* be black, not that it *must* be black.

Now we try a 1 in c6. (Make sure to try it in both directions.) Both directions fail, and therefore we have proven that it *cannot* be black, and so we can mark it white.

Going across we find a whole bunch of positions where they cannot go. Once we have ruled out columns 6-9 and 12-14 we can stop as at that point one of the 1s is forced to be in r12c5. Then LL to finish.

Found to be solvable with deep lookahead by infrapinklizzard.

This was neat because I knew how it should look, but proving it was a fun exercise. There are a lot of intricate pieces but nothing too mind-blowing.

It took me all of 6 seconds. The 5s place immediately. Seeing the near-symmetry of the clues, along with the title, I then placed the 4 straddling the midline, and zigzagged the rest.

Show: Spoilers

Goto next topic

You must register and log in to be able to participate in this discussion.