## Marking up the intelligent way

Advanced methods and approaches for solving Sudoku puzzles

### Marking up the intelligent way

At the start of each Su Doku solving it isn't necessary to mark all the candidates in each relevant cell. Quel ennui !!!

First, simply work from 1 to 9 up through each of the three stacks and then, when you have finished the stacks, left to right across each of the three bands, entering any singles and only marking up doubles (eg 7 goes either in this cell or this one, 6 or 7 goes in this cell) not trebles etc. In other words, don't mark treble etc cells at all. Second, then repeat the process a sufficient number of times to reach the point where you have either solved the puzzle or you need to employ additional techniques (see the admirable angusj.com et al). Only then consider marking up all the candidates but, here again, it may not be necessary because you can perhaps hold the limited information you need in your head. In other words, only use full marking when all else fails (in my experience not very often), at which stage there shouldn't be all that many cells to mark.

Don't give up on Su Doku - relax and use your brain to simplify it all.

Nota Bene. Marking up in the actual grid is a pain and a half unless you are working in eg a spreadsheet which you are using as a "piece of paper". Use the area around the grid intelligently instead. Then the grid is always clean and uncluttered. If using a spreadsheet as indicated, I mark "7 goes here or there" as 77 in each of the two cells and, obviously, mark "6 or 7 goes in this cell" as 67.
9X9

Posts: 100
Joined: 26 September 2005

Hmmm...how to respond without sounding sarcastic - nope, can't.
Karyobin

Posts: 396
Joined: 18 June 2005

Splendid. For the average grids at least. Then you need to talk to blokes like karyobin etc to find the way through.
stuartn

Posts: 211
Joined: 18 June 2005

Thank you for the replies. Many people complain about the laborious chore of marking up and I don't want to lose them from the Brother&Sisterhood of The Grid, simply because they find Su Doku So Dullku !!!
9X9

Posts: 100
Joined: 26 September 2005

As an Addendum to the simplified marking up method I outlined at the start of this thread, there is an avoidable trap which you can, however, unwittingly set for yourself when you are using the method, if you are not alert to it.

If eg you firstly mark each of two "6 goes either here or here" cells as 6 and 6 respectively and then each of two "7 goes either here or here" cells as 7 and 7 respectively, and this involves less than four cells in total because one or two of the relevant cells are shared, then the shared cell or cells will be marked 67 (NB ascending order).

There are then two possibilities. Firstly, 6 and 7 are the only candidates in the shared cell or cells, in which case there is no problem. Alternatively, 6 and 7 are not the only candidates in the shared cell or cells, in which case the 67 marking may lead you into subsequently assigning the wrong single value to the cell. To avoid having to therefore mark up the additional candidate(s) in the affected cell or cells, which would defeat the object of the simple method, but to alert yourself to the trap, mark the shared cell or cells 76 (ie descending order). You are then aware of the existence of other candidature.

If, through subsequent elimination, a "76" marking needs to become a "67", then you alter it accordingly.
9X9

Posts: 100
Joined: 26 September 2005

Interesting. I too have been aware of the trap you can easily set for yourself if you use a simplified marking system (having fallen into it several times at the start). I just trained myself over time to be very conscious of the fact that my marks meant "these candidates can only go here and here" and NOT "this cell has only these candidates"...

There's a lot of that kind of twinned thinking in Sudoku... I'm sure the logicians have a name for it -- distinguishing solving a cell because only one candidate can fit there, versus solving a cell because of all the cells in its domain, only one cell takes that candidate. I have to remind myself all the time that both of these complimentary ways of going about it need to be tried.

I don't think your technique would work for me with the system I currently have going, because I don't check the candidates initially in numerical order -- I tend to go by intuition of which numbers are likely to produce more results. (Doing those numbers first will increase the odds that filled-in cells that result are going to produce more satisfactory results in the next candidate you choose.) So my marking isn't naturally in numerical order to start, which would cause me to spend time putting it in numerical order, so that reverse numercial order would have significance... you see how that would go.

The one thing I do do that relates to this issue is this: if I have a puzzle that can't be solved entirely with simplified marking (ie, if I have to start marking all possible candidates for some domains at least, if not the whole puzzle -- most puzzles I do these days require that), I put those marks in a different place than the marks that indicate only-two-possible-candidates. In my case, the simplified marks go in the lower right corner, and the more involved marks the upper left. So even when my board gets cluttered, I can quickly see when I've solved a cell by eliminating one of only two possibilities for a candidate.

But that's just me -- marking systems can be quite idiosyncratic. Kind of interesting, though, to hear about systems others have come up with on their own, and to consider the strengths and weaknesses of different approaches. I hope more people start talking about their marking systems in time to come. Or are many people here using computer programs that automatically fill in all the possible candidates for them? To me those programs seem to take away a lot of the fun of the game -- it becomes more pure-logic and less a logic-and-strategy-combination. Give me a pencil and paper any day.

(Hope that wasn't a terribly controversial statement )

best,
KP
Katprof

Posts: 6
Joined: 27 September 2005

KP - As you say, different strokes for different blokes.

I agree about the "impurity" of using computer marking up. Others don't though - different strokes again. I either use pen, tippex occasionally (!), and paper for eg Wayne's Fiendish in the Times itself or a related book, or else a spreadsheet doubling as pen and paper on my laptop.

As to whether it's true pen and paper or laptop on any particular day, that depends on where I start the puzzle. If it's the breakfast table it's the laptop, if it's another particular room in the house it needs to be pen and paper. Gives a whole new meaning to the term pointing device!
9X9

Posts: 100
Joined: 26 September 2005

Katprof: I currently do it much as you do, with a slight difference. On the first rapid go-through, while entering any big numbers, I also enter any doublets (not pairs, rather, the same one number in two cells), but only if they are in one box, and in the same row or column. I enter these in the upper left, and there are usually quite a lot of such entries, some overlapping with other numbers, but not true naked pairs unless two of each.

Why bother? Because they come in very handy later in several ways, especially in denoting one form of "blocked candidates" as defined by angusj. And because they speed up things later when I pencil in all candidates, which go along the bottom of the cell, but which I don't do until much later, if at all. And, because I couldn't possibly keep them all in my head.

This works so well for me that it's the main reason I've not gone over to automatic pencilmarks via software. It's also so quick and painless that it's sort of soothing to do, part of sinking into the game. And, it provides a welcome sense of getting somewhere, when only few big numbers show up on the first pass.
Doyle

Posts: 61
Joined: 11 July 2005

Doyle --

AHA! I misspoke, because actually I meant what you've said -- it's doublets, not pairs, that I mark in specially at the outset.

(ai yi yi the terminology issues)

So it sounds like you and I are both employing the same very helpful initial technique. It does seem to "uncover" issues quickly later on if you've done this step first off, I agree.

(with an inconsequential difference: my upper left is your lower right and vice versa)

Anyone else out there to add to the marking technique discussion? Is what Doyle and I are doing the best pencil-and-paper version out there, or are there other interesting versions or refinements?

I have been experimenting with a way to mark when a candidate fits in only three cells in a block but those cells are all in a single row or column -- even though that's more than a doublet, it seems like valuable information that would be good not to visually "lose" in the mess of markings later on.
Katprof

Posts: 6
Joined: 27 September 2005

oh, one other difference, of more substance --

I still mark the doublets even if they are not in the same row or column (but still in the same block of course). It's not quite as helpful as doublets that line up perfectly (and "point" to other blocks), but it can still help me see patterns later.
Katprof

Posts: 6
Joined: 27 September 2005

Katprof wrote:oh, one other difference, of more substance --

I still mark the doublets even if they are not in the same row or column (but still in the same block of course). It's not quite as helpful as doublets that line up perfectly (and "point" to other blocks), but it can still help me see patterns later.

I did that also initially, stopped when I realized the chief value was to discern blocked candidates, which need to be in the same row or column. I've considered entering trios (terminology again, not triplets), and may yet.

Good to know I'm not the only one goes this route. And independently arrived at.
Doyle

Posts: 61
Joined: 11 July 2005

stuartn / KP / Doyle - Good to read your thoughts on marking up.

It's interesting to see how personal modus operandi develop over time - what seems like a good idea being eventually superseded by something which seems to be better. A propos, I have now moved away from marking in ascending order for eg the only two possible candidates for a cell and descending order for two candidates where there are also other candidates. I now mark "6 and 7 only" as 670 and "6 and 7 and others" as 67 initially and then eg 678 6789 subsequently, as and when greater analysis becomes needed.

On a different but related topic. There were complaints in a different thread recently about "beginners" setting out their methods and thereby causing irritation to more experienced Forum members. Speaking for myself, I welcome beginners' contributions, however wayward their technical thinking may actually be and particularly bearing in mind that English is clearly not always their mother tongue. I'm sure they value, and benefit greatly from, the advice they receive here and they are surely just as much part of the Fellowship of The Grid as we are.

I remember, when I was first cutting my Sudoku teeth, foolishly tackling one of Wayne's hardest, with only a couple of successful Times Fiendish for experience, and coming to a complete impasse fairly early on - no amount of "head-banging" would produce a way forward. Happily, I was pointed at Angus Johnson's site and soaked up his "Solving Sudoku". Returning to the log jam, armed with this knowledge and with his words therein "Hidden Quads are very rare, which is fortunate since they're almost impossible to spot even when you know they're there" fresh in my mind, I could hardly believe my eyes when the very situation itself swam up at me out of my extensive array of markings. Blinking several times and then checking my markings at least half a dozen times to prove that it really was an HQ, I then followed the exclusion process per Angus and the "dominoes" then fell, one by one, to leave the puzzle correctly completed.

To say that it felt good was the understatement of the year. It was like the sensation I experienced one day as a young boy, when I stopped off on my cycle ride home from my school in rural Shropshire, to fish for "anything", and caught my first ever trout with my very first cast. The fish was beautiful and I had it for my tea!

Let's carry on welcoming and helping new blood. After all, we were all beginners once.
9X9

Posts: 100
Joined: 26 September 2005

stuartn - Interesting to read that your current (holiday?) location is Kyrenia. Have you met any local sudoki?

As an RAF officer, I spent two and a half great years in Cyprus, in the 60's, and was there when the Turks invaded and then partitioned the island. We stayed studiously neutral. Based at Nicosia, we regularly went to Kyrenia through the pass in the mountains, both before the Turks arrived and afterwards, even though they set up and manned road blocks to keep the Greeks out.

We frequented the beaches around the old town and I particularly remember a bar and kebab restaurant we used called Theo's, near the harbour - is it still there I wonder? The RAF had a sailing club boathouse on the harbourside and I used to regularly sail an Enterprise dinghy from there, out to sea and along the coast in either direction.

After my time in Cyprus, I was sent to Nairobi in Kenya and spent a glorious six months there working (and "playing" when off duty) on the airlift of oil to Zambia, caused by Rhodesia's unilateral declaration of independence and the consequent blockading of the port of Beira in Mozambique by the Royal Navy.

9X9

Posts: 100
Joined: 26 September 2005

When I solve sudokus by hand, I try to limit pencil marks to two, occasionally 3 marks per cell. I'll either enter all possible candidates for the cell, or doublets within boxes only. I distinguish doublets from all candidates with a leading dot, e.g., ".6", or ".68" for intersecting doublets.

If I don't have a clear distinction between doublets and all candidates, things get too confusing. Also, when tracking doublets, you need to know which unit they are a doublet in (box, row, or column). I only track doublets in boxes (easiest for visual scanning). I haven't figured a good manual marking for doublets also in columns or rows that doesn't risk too much confusion, so I don't track them.

I've occasionally seen 4 intersecting doublets in a box. No good solution -- I usually just skip marking the fourth doublet.
Scott H

Posts: 73
Joined: 28 July 2005

Expert Su Doki need not read.

If it's of any help to learners, I am now using a standard test for deciding in which cells I will always use full, as opposed to "doublets only", marking up.

I now opt for full marking up in cells, either when five or more other cells within the group already have single values assigned, or when that point is reached. In addition, of course and as indicated in a previous post, I may opt for full marking up in cells which fail this test, if the situation requires it.
9X9

Posts: 100
Joined: 26 September 2005