## A variety of Sudoku Variants

For fans of Killer Sudoku, Samurai Sudoku and other variants
From the 2005 Google US Puzzle Championships -- two of 22 puzzles were Sudoku variants:

Place the digits 1 to 6 into the squares so that each digit appears exactly once in each row, column and 3x2 area. Each digit appears as in an LCD. Parts of some digits ar already placed in the grid.

Place the digits 1 to 9 into the cells so that each digit appears exactly once in each row, column and outlined region, some of which will wrap between the top and bottom edges, and/or the left and right edges of the grid.
tso

Posts: 798
Joined: 22 June 2005

catilina wrote:I liked this one, though. Does anybody know a source for these "Sum Dokus"?

The TIMES T2 just started publishing them August 31st. They have a few online already here. Turns out it is called "Samunamupure" which translates as "Sum Number Place". The TIMES will be calling it "Killer Sudoku".
tso

Posts: 798
Joined: 22 June 2005

catilina wrote:I have tried the (invalid?) Sum Doku and found 3 (?) solutions.

Code: Select all
`(1)+-------+-------+-------+ | 6 8 9 | 3 7 2 | 1 4 5 | | 4 1 2 | 5 8 9 | 6 7 3 | | 5 3 7 | 4 6 1 | 9 8 2 | +-------+-------+-------+ | 1 2 4 | 9 5 7 | 3 6 8 | | 7 9 3 | 8 2 6 | 4 5 1 | | 8 5 6 | 1 3 4 | 7 2 9 | +-------+-------+-------+ | 3 6 1 | 2 4 8 | 5 9 7 | | 2 4 5 | 7 9 3 | 8 1 6 | | 9 7 8 | 6 1 5 | 2 3 4 | +-------+-------+-------+ (2)+-------+-------+-------+ | 6 8 9 | 3 7 2 | 1 4 5 | | 4 1 2 | 5 8 9 | 6 7 3 | | 5 3 7 | 4 6 1 | 9 8 2 | +-------+-------+-------+ | 1 2 4 | 9 5 7 | 3 6 8 | | 9 7 3 | 8 2 6 | 4 5 1 | | 8 5 6 | 1 3 4 | 7 2 9 | +-------+-------+-------+ | 3 6 1 | 2 4 8 | 5 9 7 | | 2 4 5 | 7 9 3 | 8 1 6 | | 7 9 8 | 6 1 5 | 2 3 4 | +-------+-------+-------+ (3)+-------+-------+-------+ | 6 8 9 | 3 7 2 | 4 1 5 | | 4 1 2 | 5 8 9 | 7 6 3 | | 5 3 7 | 4 6 1 | 8 9 2 | +-------+-------+-------+ | 1 2 6 | 9 5 7 | 3 4 8 | | 9 5 3 | 8 2 4 | 6 7 1 | | 8 7 4 | 1 3 6 | 5 2 9 | +-------+-------+-------+ | 3 6 1 | 2 4 8 | 9 5 7 | | 2 4 5 | 7 9 3 | 1 8 6 | | 7 9 8 | 6 1 5 | 2 3 4 | +-------+-------+-------+ `

It turns out I was wrong. This puzzle DOES have a unique solution. Only the last one here is correct. The problem was that I didn't state the complete rules. The additional rule is:

-- No digit may appear twice within a single numbered area.

This puzzle is a combination of SUDOKU and CROSS-SUMS. Cross-Sums has the 'no duplicate digits' rule.

I just finished reading the article in the Times. They also forgot to mention this rule. They say:

"The digits within the oddly shaped “inner boxes” (marked by dotted lines) must add up to the small number written in the top corner of that box. Apart from that, all the normal Su Doku rules apply."

Ooops. They're gonna get complaints!
tso

Posts: 798
Joined: 22 June 2005

The sooner those are in a book or in a newspaper the better
Pi

Posts: 389
Joined: 27 May 2005

### Gould/Nishio anecdote in the Times article

tso wrote:I just finished reading the article in the Times.

One tidbit in that article is ...
The master [Tetsuya Nishio] also once engaged in a lengthy debate with Wayne Gould, the compiler behind the Times Su Doku puzzles. Gould complained about a particular Su Doku puzzle of Nishio’s devising, arguing that it required a leap of more than just logic to complete. Nishio argued fiercely against this sacrilege, eventually persuading Gould that it was a puzzle with which Mr Spock would have been perfectly satisfied.

In terms of a perceived boundary between puzzles "solvable by logic alone" and all the others, the particular puzzle mentioned in the anecdote would seem to be a "near-boundary" case. Anyone know (or, Wayne, care to say?) which particular puzzle it was?
r.e.s.

Posts: 337
Joined: 31 August 2005

My description of those events is a little different to Tetsuya Nishio's!

You can read my account in this post, made back on 1 April 2005: http://forum.enjoysudoku.com/viewtopic.php?p=442&#442

- Wayne
Pappocom

Posts: 599
Joined: 05 March 2005

Pappocom wrote:My description of those events is a little different to Tetsuya Nishio's!

You can read my account in this post, made back on 1 April 2005: http://forum.enjoysudoku.com/viewtopic.php?p=442&#442

- Wayne

Thanks for the link to your posting and the related discussion. You said (in the 31 March 2005 posting):

It would be easy for my program to create puzzles that demand a Nishio for solution. [...] But my belief is that such a puzzle, though valid, is unfair.

That's because I believe a puzzle should be an entertainment, not an exercise in mechanical and tedious plotting of numbers on paper.

Isn't it fair to say, then, that the Nishio-method is indeed "pure logic", but of a kind deemed unsuitably tedious for your intended audience?

It seems likely to me that in a similar way many purely logical methods are misrepresented as "requiring guessing" or "requiring T&E", when in fact the guessing or T&E is required not by the method, but by an audience unable to apply it. (Various types of "implication chains" are among these methods -- entirely feasible for those with a high enough "tedium tolerance".)
r.e.s.

Posts: 337
Joined: 31 August 2005

you could just as well argue, that puzzles which can be solved by
applying only some basic rules is just a tedious exercise
of finding numbers and applying these rules again and again,
without any own creativity.

If OTOH these rules are not sufficient, you'll have to come up
with some own ideas.
This could be : trying to put some number into some cell,
seeing how far you can go, maybe wiping it out later
when you reach some inconsistency.
But this is not just a random process. You can increase your chances
a lot by cleverly choosing the cell and the number which
you decide to put in.
And then the question is, how many nested levels you go
before giving up and trying some other branch.

This is, what makes the puzzle interesting IMO,
and not just how fast you can find the next placement
by "mechanically" applying some rules.

-Guenter
dukuso

Posts: 479
Joined: 25 June 2005

dukuso wrote:you could just as well argue, that puzzles which can be solved by applying only some basic rules is just a tedious exercise of finding numbers and applying these rules again and again, without any own creativity.

That would be an example of what I just referred to -- puzzles solvable by purely logical methods with no need for blind T&E, which happen, however, to be unsuitably tedious for Wayne's intended audience (e.g. methods using various types of "implication chains"). Such a method does not become other than deductive logic just because it's tedious to use.

dukuso wrote:If OTOH these rules are not sufficient, you'll have to come up with some own ideas. This could be: trying to put some number into some cell, seeing how far you can go, maybe wiping it out later when you reach some inconsistency.

Thats' a straw man in this case, though, since I'm referring here only to purely logical methods that do not require blind T&E.

dukuso wrote:This is, what makes the puzzle interesting IMO, and not just how fast you can find the next placement by "mechanically" applying some rules.

I agree, but I'm trying to keep a focus on the class of puzzles solvable by purely logical methods with no blind T&E. In fact it could often happen with non-trivial puzzles that after one makes a blind guess a pattern-based deduction is spotted which makes it clear that the guess was not required -- a more-thorough pattern-search would have avoided it.

The kind of puzzles that require a lot of "logical tedium with no blind T&E" are often, for many people, redeemed by the beauty of the deeper logical structures they exhibit -- structures that are not possible if the tedium level is set too low. But that's simply a different audience than the one Wayne seems to intend. (All this is just imho, of course.)
r.e.s.

Posts: 337
Joined: 31 August 2005

Dukuso --

Absolutely!

It seems like the difference in difficulty in the bulk of Sudokus published in newspapers is simply the number of naked or hidden singles available at any one time. The "logic" is no more complex than that which is used solving a word search puzzle. Most of the TIMES "Diabolical" require only this level of logic. They're not more difficult, merely more time consuming, as the solver is forced to search longer for each find. (Actually, I have a harder time solving this type of puzzle than those that are really more difficult -- because I can't keep from nodding off as there is no actual thinking to do.)

Wayne's stance that puzzles shouldn't require too much creative thinking or they're not fun, not even valid puzzles -- invalidates the existance of a vast number of puzzles in this genre -- and seemingly contradicts the opinions of the people who invented them.

When someone first attempts a Sudoku, s/he must figure out *how* to solve it as well as find the solution. A few puzzles later, s/he knows how and just repeats by the tactics by rote. A few puzzles later, unless the puzzles become more difficult, won't s/he become bored to tears? Will s/he feel clever on completing yet another puzzle by hunting for the hidden and naked singles?

Though it is true that the difficulty level of puzzles published by Nikoli and other Japanese magazines tops out long before they reach the level of many of the puzzles discussed in these forums, they publish a large number of variations within the genre, so that the solver is often able to have the experience of figuring out *how* to do it in addition to just finding the solution -- which is the point of this thread.

The recent Sudoku crase has been compared in the to the Rubik's cube fad. I'll make another comparison. The two weeks it took me to figure out how to solve the cube (be kind -- I'm colorblind) was great fun. I thought about nothing else. When I finally came up with a set of moves that would solve it every time -- fantastic! I played around for another week or so, improving slightly on the average sequence length. But soon afterwards, it became boring. What's the point of solving it from this scrambled postion or that scrambled position once I had general method? That's the situation now -- as if each day, the TIMES prints a specific randomized position of the cube and gives out booze if you can solve it. Of course we can solve it. If they want to challege us, they have to use a 4x4x4 cube (Killer), etc,
tso

Posts: 798
Joined: 22 June 2005

I think that Times fiendish puzzles hold their own as a concept (as long as they're proper fiendishes - not the recent sheep-in-wolf's-clothing difficults we've been getting), there's not need to make them harder progressively. Importantly, it wouldn't make sense as a concept for a newspaper puzzle, which has to be accessible to people who don't necessarily buy the paper everyday. It might not be suited to some of the people on this forum, but you are after all the minority. Most people don't mind it if the puzzle is essentially the same tactics everyday. After all, the crossword is the same essential concepts repeated daily (anagrams, puns and so forth) and that's lasted 75 years. (Not a perfect example I know, but never mind.)
PaulIQ164

Posts: 533
Joined: 16 July 2005

I expect that in the end we will mind if the puzzle is essentially the same tactics every day - but not yet, not yet!
emm

Posts: 987
Joined: 02 July 2005

Moschopulus

Posts: 256
Joined: 16 July 2005

Fantastic!

Especially:

12345 nanpure -- 1-5, each three times, in each row, column, and region

and

1234 nanpure -- one 1, two 2s, three 3s, and four 4s in each region, row, and column . Identical digits are never orthogonally adjacent.

I've never seen this, but I wondered if this idea would work. Also, each digit 1-5 twice in each group or 1-3 three times.
tso

Posts: 798
Joined: 22 June 2005

tso wrote:Fantastic!

Especially:

12345 nanpure -- 1-5, each three times, in each row, column, and region

and

1234 nanpure -- one 1, two 2s, three 3s, and four 4s in each region, row, and column . Identical digits are never orthogonally adjacent.

I've never seen this, but I wondered if this idea would work. Also, each digit 1-5 twice in each group or 1-3 three times.

there was no example included , so how do you know
it's fantastic ? Or did I miss something ?
dukuso

Posts: 479
Joined: 25 June 2005

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