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#1: Sylvain "WCPman" (qwerty) on Sep 6, 2008 [SPOILER]

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Wow - you found this puzzle fast - I just posted it! Sorry it wasn't very challenging for you, but I'm happy that you appreciate it! BTW, what province are you from? Unfortunately, Ontario is the only one I've visited - would love to see NB and Quebec!

glad to see your entry..lots of good ones to judge :)

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Telly, you keep spending so much time solving all these other puzzles... WE ARE WAITING FOR YOUR ENTRY FOR WC #2!!!!!!
(just a little, subtle hint). ;p

Very nice puzzle - I personally love the Canadian side of the falls (beautiful at night with the lights on it)

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ok fine. I'm working on it. :)

Woo Hoo!!! You only have 1-2 days left!

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Nice puzzle. It is solvable using some diagonal logic, you just need to figure out which sets of clues belong to which diagonals and you can solve it from there.

I am, as yet, not convinced that there really is such a thing as diagonal logic.

At least you can think of 'diagonal logic' as a shortcut for when you have clues that seem to fit the general diagonal pattern. You would normally guess-and-check to try and brute-force logic your way to a solution, but you can fairly easily match up horizontal and vertical clues to come quickly to the solution.

I used edge logic on the 5 clue in column 29 to get some dots (and some more line logic). I also used two-way logic in columns 25 and 27 to get some more dots. It solved out normally from there. Would someone please verify this, and we will get this marked as solvable with logic? Thanks.

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I meant to say the 5 clue in column 28.

I think I messed up my logic last night, but here is what I came up with this morning.

If you focus on that 5 clue in column 28 and try to place it at the top, you will be able to dot R19C28 and R20C28 with edge logic (row 21 will be invalid). You can also use the same logic on column 20 to dot R20C20, R21C20, and R22C20. After line logic, you can also dot R25C19 with this same logic. And then I'm stuck again.

OK, here is some more. Now looking at column 22 at the 5 clue, try placing it at the bottom. Notice the effect on column 21 (R26C21 and R28C21 would be dots). This makes it impossible to fill in column 21. So, R28C22 and R29C22 will be dots with this logic. R27C22 is also a dot with line logic now.

I next looked at columns 21 and 22 together. Notice that in row 21 that only R21C21 OR R21C22 can be filled in, but not both. The same thing applies for row 23 (R23C21 OR R23C22, not both). We know the 4 clue is connected to R22C21 and the 5 clue is connected to R22C22. With this we know that either the 4 clue will go up and the 5 clue will go down, OR the 4 clue will go down and the 5 clue will go up. This means the 4 clue will either be in rows 19-22 or rows 22-25. The 5 clue will either be in rows 18-22 or 22-26. In either case, R26C21 will have to be a dot.

OK, there is a way forward, but too much to keep in ones head though I think. So I would vote to keep it as guessing.

Gator says, in comment #19, "If you focus on that 5 clue in column 28 and try to place it at the top, you will be able to dot R19C28 and R20C28 with edge logic (row 21 will be invalid). You can also use the same logic on column 20 to dot R20C20, R21C20, and R22C20."

He is right, but I also eliminated R23C20 with the latter step and found R21C28 not classifiable at this stage, so left it unmarked. You now have one square found in C28 (R25) and two squares found in C20 (R26-27). Both blue 2s can be placed in R22 now thanks to some tricky edge logic eliminating C29R22-23 (try filling either, and solving every which way - this elimination is absolutely the key to solving this one), and C18-21 are completed. Partial solving through C24 is possible, then look at R21 for the next step. C27-29 and R21 now solve themselves, and a final look at R24 at a blue 2 will complete C25, leaving the puzzle solvable without further hints.

Interestingly, I considered the puzzle mockingly easy at first with all the easy work using the green and black markers, and even the top blue section. When I bumped into the blue on the right side, I ended up skipping this puzzle and doing 3417 before coming back. I actually looked at Gator's hint after deciphering C28 myself, and my new hint on C29 above, and had looked at C20 as well but thought I dotted a square incorrectly and got frustrated, making me look. =) But the above is now a definitive solving guide starting from Gator's hints in comment #19, ignoring #20. Please correct me if I am mistaken. Either way, the puzzle IS solvable, guessing isn't needed, just very skilled edge techniques. I'm giving it a 5 for difficulty after I fill it in on the site. Jan, please eliminate guessing from the classification of this puzzle after following this solving guide.

I agree on R23C20. I cannot agree on R22C29 and R23C29 though. It requires looking many moves ahead to eliminate those cells. We are limited to two moves look ahead.

I went back and re-did what was done on #20, and I'm going to mark this one solvable now (I originally did this over a year ago). This is a form of affirmation logic where you are examining all possibilities, but looking no more then two moves ahead for each possibility. It defines a logic constraint that must be true, namely that R26C21 is a dot for all possibilities.

Found to be logically solvable by Gator.

Actually, Gator, I had worked with the 2 in column 29, and found that the lowest possible place I could put it worked, but each of the three placements above caused it to be unsolvable, meaning the third and fourth squares from the bottom of the open area of C29 had to be untrue. I did it before C20 and C28, but this remains the step that led me to completing the two 2s in one of those two rows where I marked an untrue square and led me to the solution without any further edge logic. The solving in C20 in comment #19 actually is slightly more complex because it's not on the edge at the time it is solved, even in the hint. I used pure edge solving, and it was when I tried to complete the row segments in my envisioning that I found C28 not working in each of the three cases.

I think it still works under the edge technique solving, but it's possible that maybe I had to step into C27 once or twice. If you'd like, I can generate images, I might have muddled up some of my solving steps, but I can prove the falseness of those two squares in solving.

I still don't understand how you did your elimination in column 29 with the 2 clue without looking more than 2 moves ahead.

All right, let's forget the 2 in column 29 for a moment. Using the C20 and C28 tips, and solving as far as you can, I noticed something with R22 (blue squares are 2,2,1,1). If you assume the two leftmost squares are false and fill the rest of the row the only remaining possible way, the following occurs:

- R18C27 - empty (if true causes 5 with the blue square below, can only have 4)
- R18C25 - filled (forced)
- C25 - invalid, four cannot fit, blue squares too far apart and again would form a 5 where a 4 is the clue)

Therefore, I can herein conclude R22C18-19 are filled as before (I already filled C21-22 in the same row with basic solving and the C20 hints); I might have been lucky with my C29 attempts, but this is the same row I solved with that on paper, and this seems easier. Yes, this goes maybe a third step with the analysis but is still not too hard to work out. After these two squares get filled, the puzzle solves without any other tricks or heavy thinking.

Now back to my on paper method. C29R22-23 can be eliminated. Here's how I got there, with all presumptions being in C29:

- R23-24 filled; C28 fills R25-29, and solving C27 leaves R24C26 as a naked single making the column invalid. This does not eliminate R24C29, but is a strike against R23C29. Note that we do not need to eliminate R23C29 to solve the puzzle, but I'm pointing out that we CAN eliminate it with the next step.
- R22-23 filled; C28R25-28 also fill, logic solves the 4 in C27, and a dot goes into R21C27. We've now dotted R21C27-29, and this leaves R21 with no solution after applying the C20 hints. R23C29 is now eliminated as false and we have a strike against R22C29. (Incidentally, I believe this happens with the prior example as well but isn't necessary because we get the naked single in C27 first.)
- R21-22 filled; this one is easy to see, the dot in R22C28 and filling R21C28 leaves the 5 in C28 with no solution. R22C29 is now permanently false.

And thus, two squares in C29 are eliminated. This will also solve R22C18-19, the same squares solved in the other hint above. Once again, it logically solves after this and with no further edge logic in C29 or elsewhere.

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