Do you have any psychometric data, eg, range of solution times, on Su
doku? Might it correlate with other non-verbal reasoning tests such as
Raven's Matrices, since reviewing alternative conditional probabilities
seems to be required? Name and address witheld
No, I don’t have any data, I’m sorry. And I’m not aware that anyone is doing
any studies. Mathematicians have studied Latin Squares (the probable origin
of Su doku), but I don’t think psychologists have studied it.
Most people’s solving times improve with practice. On the other hand,
empirical observation suggests there are people who are obviously
intelligent (by non-scientific measures) and successful in their careers,
who seem to have a “blind spot” when it comes to Su doku.
Any advice on setting Su doku puzzles and determining how difficult a
puzzle will be? Michael Ruddy, Middlesbrough
My experience in solving puzzles by hand is limited, so I cannot really
comment. However, when it came to writing the Su doku computer program
(available at www.sudoku.com) one of the hardest things was making puzzles
“true to label”. It probably took me about a year to achieve. What I mean
is, a Very Easy puzzle must be very easy, and obviously different to a
Medium puzzle, or even an Easy puzzle. This would have been easier to
achieve if I had removed from myself the burden of generating the puzzles
randomly.
How do you make sure that a particular puzzle has a unique solution?Helen Restall, Guildford
Every one of my Su doku puzzles can be solved using logic alone. In practice
some people may solve them using guesses or trial and error, but regardless,
every puzzle is capable of being solved with logic.
This means the solver should be able to say, every time he or she enters a
number in the grid, “I can prove that the number I am entering must go in
this cell, and that no other number can go in this cell.”
If you can honestly say that about every number you enter, then all the cells
of the grid contain numbers that can go nowhere else. If each cell in the
grid is “uniquely correct” (to use a dubious phrase), then the grid as a
whole must be.
I wondered how many possible different sets of final numbers there are
in the 9x9 grid. I have calculated a figure but I think it is too large. Has
anyone determined this figure? David Towers, Nottingham
I have seen attempts to do this on Japanese websites, but as my Japanese is
not very good I was not able to follow along. It became apparent, however,
that there were just so many zeroes that one lost touch with the reality of
how big the numbers were. Also, it seems that there are differences of
opinion as to how the number should be calculated.
Consider, however, the number of possible solutions. That’s a huge number for
a start. Then consider the number of puzzles which can be derived from each
of the possible solutions...
Can I buy a book of Su Doku puzzles? Kim Uphill, Reading
At the moment there are no books available in the UK, but this will probably
change soon. Keep an eye on the bookshop shelves next year. When a book is
available, an announcement will undoubtedly be made on www.sudoku.com, if
nowhere else.
In Japan, there are 25 or so books or magazines of Su doku puzzles published
each year. I have about 130 such books in my own collection.
Is there a mathematical strategy behind setting the puzzle? Phil
Ashworth, St Albans
There is a connection between maths and logic. It becomes evident the higher
up you go in the study of mathematics. Some say that maths and logic are the
same thing. However, I prefer to view it as a logical strategy, because I
think it is more accessible as a logical puzzle than as a maths puzzle.
You can set Su doku puzzles “by hand”, if you want to, though I haven’t done
it much myself. You use much the same skills you do when solving a puzzle,
but backwards.
Hand-set puzzles, or puzzles set by unskilled solvers, tend to lose symmetry.
Have you noticed that the puzzles in The Times are symmetrical?
That is, the clue-numbers are not just irregularly scattered, but follow a
symmetrical layout. To the Japanese eye, a puzzle must by symmetrical to be
“beautiful” (their word). Of course, The Times being The
Times has only beautiful puzzles!
I have spent a couple of days writing a program to assist solving Su
doku, with indication of possible entries and error checks. I load and save
the problem to file. Do you have a standard file format for Su doku problems?Alan Lloyd, Marnhull Dorset
There is a standard file format associated with my Su doku program (see
www.sudoku.com). You can enter any Su doku puzzle, such as the ones you
prepare yourself, into the Su doku program. I call this, “dubbing” the
puzzle in - you just point-and-click with your mouse to enter the
clue-numbers. Once you have your puzzle in the program, you can save the
puzzle. It gets saved in the standard file format, as a .sud file. You can
then email the puzzle to friends, swap it on disks, or load it to the
internet for others to download – but of course they need the same program.
That’s the answer if you are asking about individual puzzles. If you are
asking about collections of puzzles, then you should read up about “library
books” in the Help files of my Su doku program. Library books are based on
an open standard, which is fully described in the Help files (see “Creating
library books”). In reality, a “library book” is an XML file which is
readily exchangeable. It helps if you know XML, but it’s not essential. The
necessary files are fully commented.
I completed today’s puzzle in 11 minutes - Thursday November 18. What
is your best and world record? Just to give an aim. Richard
Hime, London
Everyone has a different experience. But however long they take you for a
start, you will get your times down quickly.
My own times are probably quicker than most, because I’ve had an awful lot of
practice! (writing the program, if nothing else). However, as a guide, these
are my usual times. Very Easy - about thee minutes; Easy – about five
minutes; Medium - about ten to 15 minutes; Hard – about 25 to 35 minutes;
Very Hard – I don’t try them very often!
Beginners would probably double or triple those times.
My wife can solve them faster than I. She is something of a freak, I think (in
this respect only, I hasten to add!). The other day she did a Very Easy in 1
minute 33 seconds, and was dissatisfied with it. She got lots of practice
when testing out my theories when I was developing the computer program.
I was wondering if you could offer some tips on how to solve the "Hard"
Su doku puzzle published when the article about Su doku was first published
- November 12. Raj Malalgoda, London
One difficulty about that is, I don’t know the point at which you got stuck.
The Hard puzzle had 55 empty cells. That means you had to achieve 55 minor
victories, to get the grid filled. Each one of those 55 scenarios has its
own little tip or trick.
However, what I can suggest is this. You could dub the Hard puzzle into the Su
doku program, solve it as far as you can and then save the part-solved
puzzle. You could then email me at stumped@sudoku.com and attach the .sud
file you just saved. I will then email you back with the next step. That
might get you past an impasse. I will only give you one step, however. The
rest is up to you!
I don’t promise a same-day service. My other work will have to come first!
Also, to stop myself from being swamped, this offer applies only to the Hard
puzzle published in The Times on November 12.
How do you ensure that there is sufficient information to solve the Su
doku puzzle? Elizabeth Barker, Glasgow
See answer 3, about ensuring that the answer is unique. The Su doku setter has
to ensure that there’s enough information to ensure that each cell (forget
about the grid – it will take care of itself) can be filled in.
Su doku puzzles usually have between (say) 26 and 32 clues. Very Easy puzzles
have more clues than are actually needed to solve the puzzle. On the other
hand, some higher-grade puzzles have as few as 24 or even perhaps 22 clues.
It is possible, though rare, to have 20 clues. I have seen one puzzle (and
one only) with 18 cues. In symmetrical puzzles the number of clues is not
always an even number – it depends whether the central cell has a clue.
The number of clues can give an indication as to how hard the puzzle may be,
but it is no more than an indication. I have seen a puzzle with 22 clues
that was Easy, and a puzzle with 30 that was Hard.
Since you introduced this new phenomenon of Su doku, I have become
obsessed. On the very hard ones I seem to get so far and then run out of
ideas for solving. I am obviously missing some of the techniques for
solving. Do you have any further tips, which I believe are not on the
website you recommend? Name and address witheld
Yes, Very Hard puzzles do need some tips and tricks which are not mentioned on
the How to Solve pages of www.sudoku.com. But then, they are Very Hard
puzzles, aren’t they, and I wouldn’t want to spoil your thrill of
discovery... Well, maybe! Seriously, part of the pleasure is in charting new
territory (new to each solver, at least) and discovering new techniques.
My guess is that you probably got ten clues entered in the grid before you
could go no futher. It’s at that stage, in this particular puzzle, that the
logic suddenly gets hugely intricate.
I extend the offer made to the Very Hard puzzle, not just the Hard puzzle,
published in The Times on November 12.
I have found, however, that explaining even simple logic can take a lot of
words! and this is certainly not simple logic. So please be prepared to wait
several days for the reply.
Also, I should mention that a Very Hard puzzle is only very hard if you apply
the self-discipline of solving it with logic. If you are prepared to guess
or use trial-and-error, a Very Hard puzzle may be no harder than a Hard
puzzle.
Su doku is an interesting game, but effectively it is relatively
one-dimensional and rules-bound: once you have done a difficult Su doku the
intellectual challenge of the next tends to wane. Isn’t it the mathematical
equivalent of a maze, which also provides less enjoyment once you have
solved it? Name withheld, London
Yes, it’s curious, isn’t it! As a matter of cool analysis, I might well agree
with you. And yet person after person tells me that they are addicted (their
words) to them. I myself can recall many times when I’ve said to myself “I
really have to get on with other things when I’ve finished this puzzle”. But
when I do finish it, I feel so euphoric that I start another puzzle at once.
Others may be able to explain it more scientifically, but I think solving a
puzzle fulfils some psychological need.
Su doku is great fun, but why not a difficult one on Saturday when
there is time to work at it? Monday to Thursday all took 15 minutes or less,
though Friday was much more enjoyable at about 45 minutes. Anthony
Wagg, Banbury, Oxfordshire
Why is there no Su doku in the Saturday Times? It's great! Mike
Corner-Jones, Andover, Berkshire
Good questions! It’s not for me to say, but maybe there will be a good answer
soon!
I found the first couple of puzzles relatively easy but was flummoxed
by Friday's. I got a 6 in column 2, a 4 in Column 6 and a 5 in Column 7 but
I just could not move on from there. Can you please tell me what the next
step should have been? Simon Fowle, Watford
To Simon: For you only! If you follow the suggestion set out in my answer to
Q9, I could send you your next step. To everyone but Simon: Sorry, I have to
limit this service. If I did not, I fear would be inundated and have no time
for my day job!
