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29 April 2009 @ 06:59 am
Art of Competitive Sudoku - Czech Edition  
So, in addition to test-solving several countries' national championships, I was afforded the unique opportunity to write some championship puzzles by the captain of the Czech team earlier this year. Now that those championships and the WSC are all over, I thought I would share my contributions here. None are classic sudoku - no one asks me, or pays me, to write those - but these are all good competition-difficulty puzzles and rather cool in my mind.

1. Multiple Sudoku - this is the only new type I conceived specifically for this championship. It is one on that list of hundreds of variations I keep in my notebook as things I might do but so far haven't seen. This one does not let you write a digit-less or even single digit grid so it is not as nice as consecutive, but is still a good sudoku for solvers.

Fill in the grid with digits 1-9 (1-6 in example) so that each digit appears just once in each row/column/region. In any pair of two adjacent digits, if one is a multiple of the other, this is marked with an X. If there is no X, then the digits are not simple multiples of each other.


Solution of Example


2. Tight Fit Sudoku - this puzzle was initially inspired by a Czech creation using 1-12 that was going to be in the WSC2 playoffs but ended up being skipped. It is the first section of Mutant Sudoku, and is a very commercial and fun variation of sudoku. In fact, since it was conceived and written, it has reappeared (with different formatting) in the Tetsuya Cup this year and as a 1-13 variation on a 9x9 grid at the recent WSC. So, it seems to be a pretty commonly rediscovered idea.

Fill in the grid with digits 1-9 so that each digit appears just once in each row/column/region. In the cells filled with a slash, two numbers must be entered and the smaller number is always above the larger number.


Solution of Example


(The easier first puzzle was the one chosen by the organizers for the competition but both are good and should whet the appetite for more in Mutant Sudoku)

3. Shape Sudoku - another Mutant Sudoku type with no digits ever given in the grid. The inspiration for this puzzle came from my own Ship Sudoku in the front of Battleship Sudoku, which a lot of people liked. This grid was set to match the CZ theme and the ridiculous grids that will occur in Mutant Sudoku are hardly spoiled by revealing this type in the form of this puzzle.

Fill in the grid with digits 1-9 (1-6 in example) so that each digit appears just once in each row/column/region. Numbers should be assigned to the shapes presented in the grid based on the pieces given outside. These pieces may be rotated but not reflected, and each piece is used exactly once.


Solution of Example


4. Color Sudoku - my favorite creation of 2008 and one that I really want to use whenever I can (limitations of color printing are the big reason why I can't). I've improved the format I originally used here by adding in circled cells for when the givens provide clues to one of the primary grids. This aids solving by the color-blind, and here, makes the CZE theme pop from the page.

Fill in the three grids with digits 1-6 so that each digit appears just once in each row/column/region. In the upper-left grid, numbers are given which represent the sum of clues in the indicated colors. A Red/Yellow/Blue number is a simple given in the corresponding grid. A secondary color (Orange = Red+Yellow) represents the sum of the numbers in the Red and Yellow grid. A digit in black represents the sum of the numbers in all three grids. No digit can repeat in the same place in two puzzles. This means an orange 4, for example, could be a red 1 and a yellow 3 or vice versa, but not a red 2 and a yellow 2.

Example (the example here is a simplified form of a color sudoku from my original set - go there for the better and harder version of this puzzle):

Solution of Example


So, enjoy these puzzles. This set should certainly be a good palate-cleansing round after what we just experienced.
thedan on April 29th, 2009 11:13 pm (UTC)
Maybe I'm doing something wrong, but doesn't the CZ Shape Sudoku have two solutions? I get a 1/4 in columns 3 & 6, rows 4 & 5.

All very nice, as always. I like the circle notation for the color sudoku, both because it makes it easy to print out in B&W, and also because it suggests a more general variant style that could be expanded (for instance, to more than three component puzzles).
motrismotris on April 29th, 2009 11:23 pm (UTC)
Shoot. You are correct. My logging of files from last january (these were written before Mystery Hunt) kept an old version up even though the correct one got to Vita.

The 4395 S piece should be a 4394 S piece and with that change, the 4545 flop in rows 5 and 8 clears the 14 problem above.
motrismotris on April 29th, 2009 11:28 pm (UTC)
Fixed image is now posted, now to represent the actual puzzle used on the qualifier which was unique.
thedan on April 30th, 2009 02:32 am (UTC)
Well, between that and Devil's Kenken, I guess we're even now. ;)
grandpascorpion on April 30th, 2009 04:15 am (UTC)
Color Commentary
Hey Thomas,

I don't know if you have considered something like this but I was thinking you could represent "color" in a different way where color printing isn't possible. For instance, numbered squares could have up to 3 small blacked squares embedded along the top of each.

Sample rep:
Yellow = Left
Blue = Center
Red = Right

Using a scheme like this, it would be easier to rep a puzzle with additional "colors". For instance, small blackened squares in each of the four corners could represent a different color.

The sub-square sizing and spacing could be tweaked for clarity and aesthetics.

This is just a workaround of course. The colors are much more appealing.

cyrebjrcyrebjr on May 1st, 2009 04:09 am (UTC)
Nice multiples
I did a little survey of 1-n spectra for Multiple Sudoku of side n. It turns out that while 9 doesn't allow for a single-digit grid, 6 does.
|   *   *   *   *   *   |
|     *   * |         * |
|   *   *   |       *   |
|   *       | 3 *   *   |
| *       * |     *   * |
|   *   *   *           |
|   *   *   *   *       |
| *       * | *         |
|   *       *   *   *   |

The other values greater than 4 that might work with a single clue are 10 (4 or 8), 12 (7 or 11), and 15 (11 or 13).
motrismotris on May 3rd, 2009 02:31 am (UTC)
Re: Nice multiples
Cool analysis. It's actually a somewhat fun thought problem as you deal with un-matched primes and undiscriminated factors of 2, at least for smallish n and consider the topology space of the linkages that exist to find similar points. 14, for example, is a bit deceptive as a fail but with both 11/13 and (5+10 and 7+14) equaling two indistinct spots, it indeed fails until 15 resolves 5/10 from 7/14.