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06 March 2009 @ 08:08 am
KenKen for 3/6/09 - Downward Spiral  
I'd originally hoped to do this theme with the new subtract/divide rules and without symbols, but the resulting puzzles were certainly ExtraExtra HardHard KenKen. Also, no one confirmed an answer on yesterday's Union Jack - too busy debating my post itself I guess - so I figured I wouldn't push things rule-wise for this Friday-level KenKen puzzle.

Difficulty: Harder 7x7.

thedan on March 6th, 2009 04:40 pm (UTC)
I did solve and enjoy Union Jack, as did a couple of my friends in the math department. Interestingly, the square they both filled in first was a deduction I never noticed.
motrismotris on March 6th, 2009 04:41 pm (UTC)
The center square?
thedan on March 6th, 2009 05:00 pm (UTC)
That's the one.

Just finished this one. I actually found it a bit easier than Union Jack, but it was very different kind of deductions; this was much more like solving a kakuro, where I just whittled away at candidates. Nice though.
motrismotris on March 6th, 2009 05:26 pm (UTC)
Before I even had the theme in mind I knew I wanted a row/column to do that. Then I thought of what kind of cross themes would be nice and there was the puzzle.
standupphilosopherstandupcanada on March 6th, 2009 06:25 pm (UTC)
Agreed, very kakuro-ey. However I hope this becomes a daily publication on the blog Thomas as Nikoli is now blocked at work for me - time to hand out some CVs.
ericberlin on March 6th, 2009 05:19 pm (UTC)
I also found this one nice. By which I mean, I was actually able to solve it.
lunchboylunchboy on March 6th, 2009 06:35 pm (UTC)
I also started with the center square of the Union Jack puzzle. I enjoyed the long-distance interactions of this one, with the sums wrapping around the corner forcing interrelations of cell values (e.g., x for the upper left cell, x+2 for the last cell of row 2).
motrismotris on March 6th, 2009 06:41 pm (UTC)
I'm glad you all discover the things I put in when writing it. Even without the theming, this is why hand-construction is so much better.

For Downward Spiral, I didn't have a ton of control, but I wrote 3 or 4 puzzles until I had one I really, really liked with the interactions you describe (as well as a fun step you can take with 10+ to put in a 1.
owens888owens888 on March 6th, 2009 07:49 pm (UTC)
I solved yesterday's puzzle...
devjoedevjoe on March 6th, 2009 09:43 pm (UTC)
Another challenging one.

The 1 can be immediately filled in, as can the 7x (1,7,1) and 4/ (4,1).

If the 10+ does not contain a 1, it has 2,3,5, but this leaves no possible answer for the 9+, so the 10 does have a 1, which must go in its left cell.

The 5- cannot contain a 1, so it is 7,2 in some order. Since the 6+ cannot contain a 1, it must be 2,4, and the 3rd column already has a 2 so the 4 goes to the left. The 3/ cannot contain a 1, so it is 6,2 in some order. And the 18 is 3,6 in some order. The 8+ cannot contain a 1, so it is either 2,6 or 3,5 in some order.

The left column must be a complete set of 1 to 7 and so add to 28, so the other two cells in this region have to add to 10. Now look at the 2nd and third columns. The third column has 4,7,2,1 already placed, so the remaining cells must be 3,5,6. The bottom cell cannot be a 5 (since it would require another 5 beside it) so it is either 3 or 6, making a 7 or 4 beside it. The 11+ in the second column can only be 5,6 or 4,7, but 4,7 blocks any way of filling the bottom cell in the column, so it is 5,6. This forces the 12x to be 3,4, with the 3 on top, and we have 7,3 in the bottom cells of these columns. The top of the second column is 2, by elimination, and the two unspecified cells in the 3rd column are 5 and 6. The 10+ cannot contain the 5 since it would force a conflicting 4 in the last cell, so it has a 6 and the 5 goes on top. Then the 14+ can be completed with a 7.

Since we now have two 6s in the 4th and 5th rows (in the 11+ and 3/), the 8+ must be 3,5 in some order, and the 6 must go in the top cell of the 18x; this forces the known digits into specific cells in the 11+, 3/, and 8+. Elimination fills the 4th row and 3rd and 4th columns, and then the 2nd row.

The unfilled cells of the 16+ add to 11, so the first cell of the first row must be 3. This forces the remaining cells in the 3rd row. Now the rest of the grid can be filled by elimination except that the 9+ clue is needed to determine the ordering of the lower right 2x2 section.

motrismotris on March 6th, 2009 09:47 pm (UTC)
Great summary. You also observed my favorite step about the 10+ really early on which is why this puzzle ended up being chosen over many others that just weren't as interesting (but still were downward spirals).
Robert Hutchinsonertchin on March 6th, 2009 11:25 pm (UTC)
You have officially gotten me hooked on KenKen.

Well, on *your* KenKen.
motrismotris on March 6th, 2009 11:35 pm (UTC)
Aye, there's the rub.
scotthandelman on March 7th, 2009 03:10 am (UTC)
I enjoyed both this one and the Union Jack. I'll agree with the others that this one definitely felt more kakuresque than the previous efforts. Not, of course, that there's anything wrong with that.
motrismotris on March 7th, 2009 03:12 am (UTC)
The sign of a deep puzzle type is when the solving experience can change from one puzzle to another. I'm glad this felt more like Kakuro (and happier the other didn't).
(Anonymous) on October 30th, 2016 09:19 am (UTC)
Is there the answer for the downward spiral? i got stuck!
motrismotris on October 30th, 2016 01:14 pm (UTC)
Re: hi...
You can highlight devjoe's comment above (it is concealed white text) for a walkthrough and answer.