Introducing "Skyscraper Cryptic"

Inspired by KrazyDad's "Krypto-Kakuro", I bring you Skyscraper puzzles with the added feature of using letters instead of digits for all clues.

In the attached sampler you'll find four "Skyscraper Zero Cryptics", two of size 6 and two of size 7.

Coincidentally, just as the value 1 is easiest to determine in Krypto-Kakuro, it is also the case with SS Cryptics, although for slightly different reasons, but I'm sure you'll figure that out for yourselves!

Hope these are fun - I'm thinking of making some of these Issue 15.

Jim

Hey, what a great idea! I presume that the small letters in the puzzle are actually givens, but you've written them small so that there is plenty of room to write in the actual numbers once you've found them work out.

These are more interesting with your skyscraper zero variant than they might be with regular skyscraper, since in the regular puzzle you'd have more of a clue where the "1"s were!

Gareth

Regarding the "givens", I forgot to mention them but what you presumed was just so!


It's true that for regular (not Zero) Skyscraper Cryptic puzzles the 1 value is easily determined, it is extremely unlikely that more than one symbol could occur exactly once on each of the four sides.

However, this does not mean that (the decryption problem for) regular SS Cryptics can't be hard! For larger grid sizes there is plenty of scope for challenge, and in any case it's often possible to be less than generous with the visibility clues (ie. not give them all).

I can generate them in both regular and Zero flavours, so I'll knock up some regular examples for you.

By the way, some future offerings I hope to provide involving Skyscraper Zero:

• Skyscraper Zero 10x10 with Jigsaw/Regions

• Samurai Skyscraper Sudoku Zero

• Samurai Star Skyscraper Sudoku Zero

Also, further down the track, a new application for Zero - I think it will make things very interesting for Killer Sudoku (and Outside Sum).

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Also, further down the track, a new application for Zero - I think it will make things very interesting for Killer Sudoku (and Outside Sum).

Oh dear, and this from a man who is allegedly a Computational Scientist!

Zero makes no difference to the complexity of a straight Killer puzzle, since there is obviously a 1-to-1 correspondence between sums of digits in range [1 to N] and range [0 to N-1]. For example a 2-cell cage with sum = 5 can be (1,4) or (2,3) in regular mode, which corresponds to a cage with sum = 3 in zero mode, with choices (0,3) and (1,2).

However while effect of zero on the puzzle itself is nil, the effect on the solver is certainly noticeable! All of the stuff you know by heart about row/col sums, minimum/maximum sums has to be re-learned.

For example, regular mode with N=9 has row/col sum of 45, and a 3-cell cage sum can be 6 to 24 - if it's 6 the values must be 1,2,3 etc etc

In zero mode, row/col sums are 36, a 3-cell cage ranges from 3 to 21, and if it's 6 the values might be 0,1,5 or 0,2,4 or 1,2,3

So while I won't be offering "Killer Zero" puzzles per se, I do have a new "Skyscraper Killer" puzzle coming in which the Skyscraper can be Zero flavoured, so watch out!

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Mathimagics
However while effect of zero on the puzzle itself is nil, the effect on the solver is certainly noticeable! All of the stuff you know by heart about row/col sums, minimum/maximum sums has to be re-learned.

I'm glad you wrote this! I published a Killer Sudoku puzzle in Sudoku Xtra a few issues back that used 0-8, and I had multiple people contact me (including one posting here) pointing out how facile this was. I argued like you, that while it may not affect the underlying maths or logical complexity of the puzzle it does in practice change the solving experience for the player. But none the less I decided to edit the issue, and replaced the 'offending' puzzle with one using a different set of numbers.

You can of course use gaps in the number range too (I've tried both odd and even numbers for example), or negative numbers (although not so much in Skyscraper!). Sudoku Xtra has featured many different sets of numbers for both Killer Sudoku and Killer Sudoku Pro. One of my favourites is -4 -3 -2 -1 0 1 2 3 4, but of course there are an infinite range of possibilities. I've also tried UK coin values, i.e. 1 2 5 10 20 50 in a 6x6 Calcudoku puzzle. In any case, they certainly all change the flavour of the puzzle.



Edited 1 time(s). Last edit at 04/26/2011 04:05PM by gareth.

I must have missed the Killer Sudoku 0-8 you mentioned, but I'd argue that it's certainly not facile - anything that requires you to adjust your thinking proceses is IMHO a good variation to the standard puzzle.