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02 October 2009 @ 12:02 am
Friday Puzzle #17 - Kakuro Twins  
There is an established crossword variant, Saimese Twins, where two grids and two sets of clues are given; deciding what clues belong in which grid is the extra challenge which makes them particularly enjoyable.

Here, that concept is applied to Kakuro. You may choose to solve this on two separate copies or just on one, but there are indeed two grids here with two solutions. Together, the two solutions will use each horizontal or vertical clue exactly once. So, for the first horizontal entry, in one grid the sum will be 10 (as indicated on the left of that row of cells) and in the other grid the sum will be 12 (as indicated on the right of that row of cells). Identifying which crossing down clues go with the 10 and which with the 12 will be up to you to determine. Also, just because the grid with the 10 used the "left" clue for the first entry does not mean it uses the "left" clue for the entry below it. Consider it equally likely (until you can prove otherwise) that that clue is a 16 or a 26 for the first grid. As in a standard kakuro, use the digits 1-9 with no digits repeating in any entry.

This puzzle is phenomenally hard, so I offer you the following "nerfed" version if you want. On this easier version, all of the cells that contain the same number in both grids are shaded pink. This should allow a few more entry points than the unhinted version. If that is still not enjoyable, I'll point you back to the kakuro puzzles thedan and I wrote for the Mystery Hunt. You may also enjoy a walk, some time with a good book, or a brand new episode of Dollhouse. Until next week, ....
TH rpipuzzleguy on October 2nd, 2009 06:36 am (UTC)
Brilliant. Looking forward to trying it.
(Anonymous) on October 2nd, 2009 08:42 am (UTC)
Wonderful, I've added your weekly puzzle to the list of puzzles I usually do. (If it's not a word puzzle, I don't like them that much.) They are very innovative and well-thought-out, sometimes super hard but still humand-solvable. This type of puzzles are hard to come by.
sheehan on October 3rd, 2009 04:23 am (UTC)
Nice puzzle. I solved it fairly linearly (switching backing and forth) from bottom left to bottom right to middle to top right to top left.

I was worried it would require two separate break-ins.
motris motris on October 3rd, 2009 04:29 am (UTC)
That's certainly my intended path. I had thought of giving another work-in somewhere else but didn't. This kind of design is complicated enough that it is quite unlikely there is anywhere else really productive to start.

I'd also thought of a more closed geometry - where region sums might become useful meta-information - but had a hard enough time writing this one that I'm not sure I'll try that concept out myself.
MellowMelon MellowMelon [wordpress.com] on October 4th, 2009 02:17 am (UTC)
Nice, and very challenging as promised. Just curious, how would you go about doing pencilmarks and such for this one? Like a previous comment said, if there were two breakins you'd have to determine later how each part syncs up, and I don't think you'd want to make 4 copies of the grid.

I tried something where each cell had a diagonal split and two numbers, with the diagonal denoting whether the clues for that cell in each grid were top-left/bottom-right or top-right/bottom-left, but it ended up too unreadable for me.
motris motris on October 4th, 2009 02:50 am (UTC)
I used the diagonal split for my second test and it worked better for me than two grids but then I knew the path ;).

One reason I did not want to have two intersecting break-ins is exactly the reason you give - how to store data without needing a lot of erasure if your coin flips wrong. This may be what you are describing, but I suppose you could write sure numbers in the top/bottom and left/right of cells and then, when regions intersect, add the correct \ or / to merge top with left or top with right, but that seems potentially too complicated as well.
Robert Hutchinson ertchin on October 5th, 2009 03:31 am (UTC)
It took a lot of work, but I did finally solve the nerfed version. With the "proper" version, I kept causing a contradiction in the lower left corner. Still don't know what I was doing wrong, but getting my sums confused seems likely, possibly by using one sum twice rather than using each once.
TH rpipuzzleguy on October 7th, 2009 03:48 am (UTC)
Finally finished the original version. Great stuff.
thesubro on October 14th, 2009 01:01 am (UTC)
A long and winding road ... to nowhere ...
Okay. I spent over a week on the full puzzle (nerfed versions are for muggles). Much of the journey was caused by the fact that I solved it linearly and I kept arriving at obvious non-singular solutions (nonsingular internally to grids, and nonsingular across grids). Each of the first few times, I figured I had made a mistake and went back to the beginning. I came to realize that it was not a singular solution (if I am wrong, let me know and I'll go back again, BUT I'm happy to share my solution grids and their documented variations).

It was a great puzzle, but would have preferred singularity - as I always do when seeking A solution. I am amazed at its creation. I used the method sort of noted above with a single grid and an "X" written into each box with possible digits in each "quadrant" that arrive at cross-impossibilities that compel limited options and then answers. Can't imagine solving it any other way. Kudos to you Sir Tom for the concept and the creation. I'd welcome another, but would prefer that in normal puzzle setting "a smaller piece of the pie," like an 8x8 or so, just that its a bit more manageable.

I appreciate this blog and puzzles like that more than you can imagine. Thanks so much.


How many could have created it?
... how many could have solved it?
How wonderful for both.
motris motris on October 14th, 2009 01:04 am (UTC)
Re: A long and winding road ... to nowhere ...
I'm only aware of the one solution across the two puzzle grids, so I would be interested to check over any alternatives you have.
motris motris on October 14th, 2009 02:09 am (UTC)
Re: A long and winding road ... to nowhere ...
Look at this possible solution file and see if you have differences.
thesubro on October 14th, 2009 03:01 pm (UTC)
Re: A long and winding road ... to nowhere ...
"Never mind"

I knew it was just a matter of time before I overstepped my bounds on this blog.

The fact of the matter is that I solved this puzzle (or more accurately stated, almost solved this puzzle) with one hand behind my back (to my own detriment). I could bore you with the details as to how I limited potential digits almost in a theoretical sense as compared to an actual sense (not seeing how they actually would form two full grids using each line sum twice) I probably took 10 times as long to get to the end that I did - which had all the right digits in all the right boxes and all the right common boxes in place, but it appeared to be non-singular. When you advised that it was singular (which I will always assume in the future unless advised otherwise) I went to actually create grids to show you how right I was. In creating the actual grids, I came to realize the singularity - and how wrong I was.

Fantastic puzzle. Had great fun with the struggle - both against the puzzle and my own inane limitations I placed on the solving process.

Sorry to distract you during your training period. Truly.

motris motris on October 14th, 2009 03:07 pm (UTC)
Re: A long and winding road ... to nowhere ...
No problems, really. I expected this challenge to be really hard and it seems, even from top solvers, that that is the case. Good job seeing it through. Difficulties for the next several weeks will be back to ~regular.
stigant on October 14th, 2009 01:42 pm (UTC)
Wow! Finally finished. Between this puzzle, skyscraper kakuro, and large-square kakuro, I hope your next book is Mutant Kakuro. I'd buy at least 3 copies for myself and gifts for others.
motris motris on October 14th, 2009 03:09 pm (UTC)
The Mutant Kakuro thought has come up before, but I still doubt it would be a very commercial title. Still, I've really enjoyed making kakuro variants and I need to find some forum to start publishing them more regularly.