motris (![[info]](http://l-stat.livejournal.com/img/userinfo.gif){kind=small} motris) wrote,@ 2006-07-22 18:18:00 |
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TWO FOR THE PRICE OF NONE!!! - Skyscraper Kakuro
So this idea is not necessarily a new one. It was actually called a "skyscraper varia" in the WPC at Eger, Hungary, but it was put into the Grand Prix (read: speed) round and was designed to be solved in ~2 minutes with mainly number-writing and not thinking. With puzzles of this type, 2-digit clues are automatic gimmes of 2 digits, and this "varia" had many entries like this. I decided at some point I would try to revisit the concept as I love mixing skyscraper ideas into other puzzle types, and so here I have done just that.
As with a standard kakuro puzzle, the numbers in each entry (either vertical or horizontal) must be from 1 to 9 and no digit is repeated in a single entry. However, this puzzle is a "skyscraper" variation of kakuro. In a skyscraper puzzle - typically a latin square - the number "n" is meant to represent a "building" that is "n" floors high. Because a tall building will obscure any shorter building behind it, the typical givens in a skyscraper puzzle are the number of buildings you can see looking in a given direction. As this is a kakuro, the clues here represent the sums of the heights of the buildings you can see. Notice that, because of the additional constraints on information, sums are now given in all directions in the puzzle (ie looking up and down, and looking left and right).
To make sure the skyscraper concept is clear, imagine the entry 69578 in a row of the puzzle. Looking from the left, you would see the 6-story building and the 9-story building (but no buildings behind the 9-story) so the clue on the left would be 15. Looking from the right, you would see the 8-story building and the 9-story building but would not see the 5-story or 7-story buildings as they are hidden by the 8-story building or the 6-story building behind the 9-story building; the clue from the right would be 17 = 8+9. As an extreme case, 812345679 would be 17 from the left, and 9 from the right. Of course, any permutation of the (1234567) buildings would also fulfill these clues, so they must be forced by the crossing clues.
I first wrote the top puzzle (avoiding all 2-digit clues, as they are too simple) but then decided I felt even that puzzle was too simple and I challenged myself to write the most "open-space" skyscraper puzzle I could, so I wrote the latin square puzzle below as well which is much closer to a skyscraper than a kakuro but I think the name still applies. On playtesting, I realized both are actually quite hard, so I post them both (just because that's the kind of person I am). BE VERY CAREFUL when placing entries in these puzzles as it is very easy, until you grasp how to do the sums, to make mistakes in these puzzles.
So this idea is not necessarily a new one. It was actually called a "skyscraper varia" in the WPC at Eger, Hungary, but it was put into the Grand Prix (read: speed) round and was designed to be solved in ~2 minutes with mainly number-writing and not thinking. With puzzles of this type, 2-digit clues are automatic gimmes of 2 digits, and this "varia" had many entries like this. I decided at some point I would try to revisit the concept as I love mixing skyscraper ideas into other puzzle types, and so here I have done just that.
As with a standard kakuro puzzle, the numbers in each entry (either vertical or horizontal) must be from 1 to 9 and no digit is repeated in a single entry. However, this puzzle is a "skyscraper" variation of kakuro. In a skyscraper puzzle - typically a latin square - the number "n" is meant to represent a "building" that is "n" floors high. Because a tall building will obscure any shorter building behind it, the typical givens in a skyscraper puzzle are the number of buildings you can see looking in a given direction. As this is a kakuro, the clues here represent the sums of the heights of the buildings you can see. Notice that, because of the additional constraints on information, sums are now given in all directions in the puzzle (ie looking up and down, and looking left and right).
To make sure the skyscraper concept is clear, imagine the entry 69578 in a row of the puzzle. Looking from the left, you would see the 6-story building and the 9-story building (but no buildings behind the 9-story) so the clue on the left would be 15. Looking from the right, you would see the 8-story building and the 9-story building but would not see the 5-story or 7-story buildings as they are hidden by the 8-story building or the 6-story building behind the 9-story building; the clue from the right would be 17 = 8+9. As an extreme case, 812345679 would be 17 from the left, and 9 from the right. Of course, any permutation of the (1234567) buildings would also fulfill these clues, so they must be forced by the crossing clues.
I first wrote the top puzzle (avoiding all 2-digit clues, as they are too simple) but then decided I felt even that puzzle was too simple and I challenged myself to write the most "open-space" skyscraper puzzle I could, so I wrote the latin square puzzle below as well which is much closer to a skyscraper than a kakuro but I think the name still applies. On playtesting, I realized both are actually quite hard, so I post them both (just because that's the kind of person I am). BE VERY CAREFUL when placing entries in these puzzles as it is very easy, until you grasp how to do the sums, to make mistakes in these puzzles.
