Is SudoKu puzzle a good educational tool?

[Jyera]

With all the rage about SudoKu, I think it is relevant to discuss it's usefulness as an education tool.

Is SudoKu puzzle a good educational tool? Is it overrated?
What can we teach using Sudoku?
Can we teach Critical thinking or logical thinking using Sudoku?
How will doing a Sudoku puzzle as an exercise help?

The above questions are just thrown to start the discussion.
Feel free to make any observation and analysis.

Here is some links:
http://en.wikipedia.org/wiki/Sudoku
http://www.puzzle.jp/keys/sudoku_keys-e.html
http://upload.wikimedia.org/wikipedia/en/thumb/f/f0/Cross-hatching.gif/200px-Cross-hatching.gif

[Alkatran]

Sudoky is a puzzle, not a teaching aide. The only use I could see for it is to make people think about the best way to solve it for awhile.

I mean, it's not really the hardest puzzle in the world: find the square that has to be a certain value and enter it.

[CFLarsen]

It's a very good tool for teaching straight logic. It teaches you while you are playing a game.

And there's no blood or monsters.

[athon]

It's a good pattern-searching game, and as long as that's all that it's being used for, I don't see a problem with it. It's not exactly mathematical, but as long as that's kept in mind...go for it.

Athon

[sphenisc]

It's a good pattern-searching game, and as long as that's all that it's being used for, I don't see a problem with it. It's not exactly mathematical, but as long as that's kept in mind...go for it.

Athon

It is exactly mathematical.
It can lead into discussions of deductive reasoning, logical syllogisms etc.
It's useful for introducing reflexive thinking about thinking, e.g. search algorithms, when do you switch from one algorithm to another?
Its a great way of developing ideas about programming, from arrays, loops and conditionals, to ideas of recursion and efficiency testing.


I mean, it's not really the hardest puzzle in the world: find the square that has to be a certain value and enter it.



Great, please complete the first two 3X3 puzzles at

http://sudoku.sourceforge.net/brain.htm

to demonstrate how easy they are. :)

[athon]

It is exactly mathematical.
It can lead into discussions of deductive reasoning, logical syllogisms etc.
It's useful for introducing reflexive thinking about thinking, e.g. search algorithms, when do you switch from one algorithm to another?
Its a great way of developing ideas about programming, from arrays, loops and conditionals, to ideas of recursion and efficiency testing.

I could use any pattern in place of the numbers. I could have a number of fruit symbols and ask somebody to replace the missing fruit. Quantification and manipulaiting quantified models is not required, which to me is what mathematics is. This is not mathematics, sorry.

Athon

[sphenisc]

I could use any pattern in place of the numbers. I could have a number of fruit symbols and ask somebody to replace the missing fruit. Quantification and manipulaiting quantified models is not required, which to me is what mathematics is. This is not mathematics, sorry.

Athon

Do you regard Set Theory as one of the arts then? :)

http://mathworld.wolfram.com/Set.html

[athon]

I've done a quick search through my text books and online to try to find a definition that might suggest Sudoku is mathematical. The closest definition I can find that might support your argument is

The study of the relations between objects or quantities. These relations are organized so that certain facts can be derived from others by using logic. from www.sasklearning.gov.sk.ca/docs/elemath/glossary.html

Set Theory, like Venn Diagrams, is useful in mathematics as a form of applied semiotics, and can be used mathematically to deduce unknown facts from known ones. I guess it all depends on what boundaries you set to your definition. Is it mathematical to deduce the missing letters in a crossword? It's not really all that different.

If crosswords are mathematical applications, then I concede. But I hesitate to make my definition for the discipline of mathematics so broad.

Athon

[Soapy Sam]

Is it mathematical to deduce the missing letters in a crossword? It's not really all that different.- Athon.

I may have you drummed out of the Clan for this. Crosswords are puzzles demanding intelligence, erudition, general knowledge and a warped mind.

My steam driven PC on the other hand can solve any 9x9 Sudoku puzzle in about three seconds, most of which is screen refresh.

I would not call Sudoku mathematics, certainly not arithmetic.
I'd call it tragically boring, actually.

[athon]

Soapy, I think you misunderstand. I wasn't equating the complexity of the two puzzles; I was saying that if Sudoku (BTW, isn't he a Sith lord or something?) is mathematical, then so are crosswords. The premise of deciding on what symbol to place in a box based on its context within other symbols in the sequence is the same as crosswords.

Of course crosswords are vastly superior.

Please, I beg you; don't have me thrown from the clan! I've only had our family tartan cleaned!

Athon

[Melendwyr]

I would not call Sudoku mathematics, certainly not arithmetic.
I'd call it tragically boring, actually. Computers can solve the Tower of Hanoi quite easily. Humans attempting it need to exercise different skills.

SuDoku is useful for developing thinking skills, but not mathematics in general. Logic, yes.

[3point14]

Hang on - a computer can solve a sudoko with (I imagine) not that complicated a programme.

I imagine it would take some pretty sophisticated software to solve a times cryptic crossword?

Sudoko must be much closer to mathematics than a crossword is, surely?

[Soapy Sam]

Tower of Hanoi personal best - 3 mins 33 seconds.

I would have been faster but I cut my finger with the hacksaw.


Yeah. Athon was being ironic.
I was being obtuse.

The point is that neither of them is a mathematical puzzle unless your definition of "mathematical" is very wide indeed.

What may be mathematical, is how do they compile a Sudoku puzzle? It's claimed there is only one answer. What's the proof of this?
Is there a reverse algorithm which should give thecorrect answer without analysing the logic of what is where? If there is only one correct answer given the numbers (or symbols) revealed, then surely it ought to be possible to solve it at a glance?

[CFLarsen]

I was saying that if Sudoku (BTW, isn't he a Sith lord or something?)

Count Doku. He's the inventor of Maze Window.

[LTC8K6]

Rage?

Where?

[Melendwyr]

Is there a reverse algorithm which should give thecorrect answer without analysing the logic of what is where? If there is only one correct answer given the numbers (or symbols) revealed, then surely it ought to be possible to solve it at a glance? No, it's not necessarily the case that there are shorter methods of determining whether the puzzle is solvable - although there may well be such methods.

The program to solve a 3x3 Sudoku is relatively simple - but the most straightforward way of writing it relies on recursion. Rather like the Tower of Hanoi, the solution is much more complicated than the natural-language description of the algorithm implies.

[drkitten]

I could use any pattern in place of the numbers. I could have a number of fruit symbols and ask somebody to replace the missing fruit. Quantification and manipulaiting quantified models is not required, which to me is what mathematics is.

LIke what sphensic said.

I would regard the sudoku puzzle as a good instance of pure algebra (and/or set theory), in part precisely because of the logical structure divorced from arithmetic.

It's mathematical because it can be so easily described and solved in a purely axiomatic framework, something that a crossword cannot be (you need background knowledge, like the meanings of words, to solve crosswords).

[Jyera]

It is exactly mathematical.
It can lead into discussions of deductive reasoning, logical syllogisms etc.

I agreed. In addition, it teaches you how not to trust guessing and wishful assumption. One wrong guess can lead to total confusion, regardless of the precise logic after the wrong assumption. It is a bit like, getting the premise wrong.

It's useful for introducing reflexive thinking about thinking, e.g. search algorithms, when do you switch from one algorithm to another?
Its a great way of developing ideas about programming, from arrays, loops and conditionals, to ideas of recursion and efficiency testing.
..snipe..

Rather than just reading other people's solution to how to solve Sudoku, I think the learner would benefit most by trying to figure out the best ways to solve a Sudoku Puzzle.

Solving the puzzle itself is mechanical.

Drafting an instruction manual on the various ways to solve the Sudoku puzzle should prove to be a good exercise in original thinking and critical thinking.

[Jyera]

I think of this way of teaching critical thinking using Sudoku.

(1) Tell some teams of students to solve a Sudoku puzzle.

(2) Assign three other students to be (a) "Crystal psyhic" (b) Guesser (c)Logicians.

Role of the "psyhic" is to provide consultation blind folded.
The Guesser provide consultation via guessing and will always give an answer.
Logician will use logic of cause.

(3) The solvers may choose to consult once from anyone of the consultant.

(4) Compiling the result should provide some useful insight.

I figured that the teams who has consulted the logician would benefit.
Those who doubted the psychic and guesser will be okay.
While those who took advise from psyhic will be misled and will "curse and swear".

[delphi_ote]

As with any puzzle like this, mathematicians and computer scientists have been interested. Here's are some results from a quick Google search:

http://www.reed.edu/~mcphailb/lightup.pdf
http://web.inf.tu-dresden.de/~bf3/sudoku/sudoku.pdf
http://arxiv.org/PS_cache/cs/pdf/0507/0507053.pdf

[epepke]

Computers can solve the Tower of Hanoi quite easily. Humans attempting it need to exercise different skills.

SuDoku is useful for developing thinking skills, but not mathematics in general. Logic, yes.

Actually, there's an iterative solution to the Towers of Hanoi that is quite simple for humans.

[LW]

The program to solve a 3x3 Sudoku is relatively simple - but the most straightforward way of writing it relies on recursion.

If you are using a traditional programming language, then yes, implementing it with recursion is likely to be the simplest way.

But if you don't limit yourself for traditional programming languages, then the most straightforward way is to use some form of declarative constraint programming.

For example, using the Smodels (http://www.tcs.hut.fi/Software/smodels) language sudoku looks like this (% is the comment symbol):

% Define the grid and possible values
row(0..8).
col(0..8).
val(1..9).
% Each cell has to have a unique number:
1 { has_num(A,X,Y) : val(A) } 1 :- row(X), col(Y).
% Each number occurs exactly once in each column.
1 { has_num(A,X,Y) : row(X) } 1 :- val(A), col(Y).
% Each number occurs exactly once in every row
1 { has_num(A,X,Y) : col(Y) } 1 :- row(X), val(A).
% Each number occurs exactly once in each of the 3x3 blocks
1 { has_num(A,X,Y) : row(X) : col(Y)
: eq(div(X,3),R) : eq(div(Y,3),C) } 1 :-
rowbl(R), colbl(C), val(A).
% Defining the 3x3 blocks:
rowbl(0..2).
colbl(0..2).

This program can be used to both solve sudoku puzzles and to generate new ones.

[Ian Osborne]

Sudoku (BTW, isn't he a Sith lord or something?)

No. Sue Doku (to use the correct spelling) was the inevitable schoolgirl character in the last Japanese 2D beat-'em-up. You know, the one with the ultra-fast moves but zero power.

[Melendwyr]

Actually, there's an iterative solution to the Towers of Hanoi that is quite simple for humans. My point is that computers have no problems executing long, complex strings of commands. There's a simple rule for the Tower, yes, but it's quite a challenge for a human being to keep that rule straight as the Tower gets taller. Even ignoring the obvious problems, I doubt a human could manage the N=64 Tower without making a mistake.

[Diamond]

Sudoku puzzles are masssive wastes of my precious lifespan.

Q: the blurb says that each Sudoku puzzle has a unique solution. Has anyone proved this?

[davidhorman]

Q: the blurb says that each Sudoku puzzle has a unique solution. Has anyone proved this?

I think it's meant to be inherent in the definition of "Sudoku puzzle". Any grid of numbers which didn't have a unique solution under the rules of Sudoku wouldn't be a Sudoku.

David

[Diamond]

I think it's meant to be inherent in the definition of "Sudoku puzzle". Any grid of numbers which didn't have a unique solution under the rules of Sudoku wouldn't be a Sudoku.

David

:monkey:

[drkitten]

My point is that computers have no problems executing long, complex strings of commands. There's a simple rule for the Tower, yes, but it's quite a challenge for a human being to keep that rule straight as the Tower gets taller. Even ignoring the obvious problems, I doubt a human could manage the N=64 Tower without making a mistake.

Actually, no.

There is a simple iterative solution that humans can follow as long as their boredom threshhold holds out. Imagine the three pegs arranged in a circle. Every other move, move the smallest disc the appropriate direction (wolog, clockwise), and in between, make the only other legal move.

So the iterative solution is as follows:

Step 1 : move the smallest disk clockwise
Step 2 : make the other legal move
Step 3 : return to step 1 until the solution is complete

[Melendwyr]

Over the steps necessary to complete the n=64 Tower, a human would probably screw up that procedure at least once. (Note: the number of steps necessary to solve a Tower of Hanoi puzzle is equal to -1 +2^N.

[LW]

Over the steps necessary to complete the n=64 Tower, a human would probably screw up that procedure at least once. (Note: the number of steps necessary to solve a Tower of Hanoi puzzle is equal to -1 +2^N.

The difference is immaterial since neither the human nor the computer would actually solve the puzzle since 2^64 is far too great number. The running time for the computer program would be measured in centuries, at least.