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#1: Joe (infrapinklizzard) on May 6, 2012

This puzzle is in response to Forum topic 325 ( http://webpbn.com/read.cgi?type=T&id=325 ) where LoloJean asks about edge logic using more than one clue.


Note: THERE IS NO PICTURE - ONLY LOGIC.

I solved a puzzle with this very thing last night. In GAMES magazine, July 2012 issue, the Paint by Numbers puzzle #2 has a situation in the top that can be started this way.

The top two rows of this puzzle are the same as that puzzle, but the rest is just gobbledegook to make the situation the same without making a huge puzzle.


To solve:

Normal edge logic (with one clue) gets you nowhere. The 4 in c1 can go in two different places with no way to choose without looking many steps ahead.

The 7 in r10 can go anywhere with normal edge logic.

The 5 in r1 can go anywhere from 8-25 with normal edge logic and the 6 in the same row can go anywhere from c1 to c19 if you only look at the 6.



[Note: deep edge logic (looking beyond the row right next to it) is similarly of no help on this puzzle. The 4 in c1 is not helped at all. The 7 can go in at least two places (ie. c2-8 and c19-25) with many steps before a conflict. And the 5 in r1 can still go anywhere in its original range except c15-19, and c16-20. (The 2 in c18 would break the blocks in r3 into unacceptable blocks for the clues.)]



Look back at my last statement about the normal edge logic. The 6 in r1 can go anywhere across the top row up to c19 *if you only look at the 6*.

However, we must remember that the 5 must still be placed in that row. If you look at the possible placements of the 5 (c8-25) you can see that no matter where the 5 goes, it will extend into the 7 in r2 for its entire length - that is, once you place the 5 in r1, five pixels of the 7 in r2 will be automatically fixed.

Since the 5 in r1 uses most of the 7 in r2, we can now see that the 6 in r1 cannot be placed in most of r1. If it crosses more than one clue in a row that extends into r2 (ie is >1), those pixels would have to be part of the 7 in r2.

In fact, if the 6 were to go anywhere but in c1-6, it would take up too much of the 7 in r2 and the 5 would have nowhere to go.

Thus the 6 in r1 can be placed and the rest is line logic.


Looking at the 6 or the 5 individually gets us nowhere, but remembering the effect of 5 on r2 when looking to place the 6 gets us going.

what about this:

el the 4 clue in c1 to get black in r2-4
ll
2-way logic on either end of that section of 3 black clues to dot a lot of squares: r2c3-5, r3c3-6, r4c3-5, r6c2-5, r7c2-6, r8c2-6, r9c2-6 and r10c2-6 (you only actually need to dot the squares from r6-r10 though)

iel on either the the 9 clue in r8 or the 9 clue in r9 (it doesnt matter which one, as either will work) to dot c7-10
ll to finish

very fun solve
no guessing (of course)

i did it like bugaboo at the start (el, ll, 2way) but my iel was in r5 and r6. there are six 5 clues in c10-15 and since, at most, five of them can go into R11, at least one must be in r10. dots C1-4,21-25R5.

Can't believe i got it .... cool one Joe

These explanations are far more confusing to me than the 5 seconds of logic I used to start this puzzle. I saw the places where the 1s had to go, and put them there. :)

Like Minesweeper, I use pattern recognition as much as actual logic.

Thanks for the comments!

bug and David - The problem with making a demo puzzle is that there's almost always another way of doing something. Especially when you want to come up with something quickly to show a single point, or are adapting another puzzle to accentuate your point (and in this case avoid copyright infringement). Thus the title and comment 1 to show the intended thrust.

Kristen - That's why I usually make visual tutorials. I find it harder to read these and visualize than I do to solve the puzzles, too. It is much easier to see the placements and ramifications than to read it and try to work it out from text. But those take quite a bit more time, and this was just a single point. And it was bedtime.

Minesweeper was very interesting for me when I was figuring out the logic. Then I learned the patterns that signaled each type of logic. (E.g. 121 means the ones next to the 2 are clear; and if it's on an edge, then the 1s are mines; 1221 has mines next to the 2s, etc) Then pattern recognition turned it into a zen activity. Eventually it was a speed-zen activity.



Well it seems it helped LoloJean, so original mission accomplished!

Exactly! (re: Minesweeper)

...223321... = 5

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Found to be logically solvable by gator.

Show: Spoilers

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