## Non-standard pencil marks

Advanced methods and approaches for solving Sudoku puzzles

### Non-standard pencil marks

I play sudoku by using a non-standard system of pencil marks.
Instead of placing a bunch of little digits which could still possibly fit into a space, I use a system of "Doubles" and "Excludes".

I find it cleaner and easier to write, and I have used the system to solve Hard and "Evil" puzzles. My system gives rise to a set of advanced techniques that I have called "pushing". Pushing happens in very difficult puzzles that contain completely empty 9-squares at the beginning (usually in the corners).

I used the "Doubles" technique on the problem posted below. I "doubled" the seven on column 8. In that post I used "m7" and "m7". I don't consider that technique to be advanced, because I use it all the time.

how-do-i-solve-this-puzzle-without-guessing-t30784.html
dokusan

Posts: 6
Joined: 03 January 2013

### Re: Non-standard pencil marks

Six is doubled here. Doubling means that 6 must appear in one of those spaces, and nowhere else.
Six is doubled with the letter m.
m6_doubled.png (2.68 KiB) Viewed 1191 times

If we later find that an 8 must go on top of an existing m6, then the remaining m6 is made into a real 6 automatically, without having to check it against the puzzle.
Automatically a 6
auto6.png (2.69 KiB) Viewed 1191 times
dokusan

Posts: 6
Joined: 03 January 2013

### Re: Non-standard pencil marks

That sounds like a great approach for puzzles of an appropriate difficulty level, but I don't think it will generalize well for puzzles that are more complex. Two other alternative approaches I have heard of are making pencil marks in every cell a given digit can not go in, and making only the pencil marks that aren't obvious from simple logic (the simple logic pencil marks being recreated in your head as needed).

JasonLion
2017 Supporter

Posts: 641
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Non-standard pencil marks

Excludes mean that those two spaces must have these two digits, and no other digits.
We know those digits must go there, and we only lack knowledge of which order they appear.
Excludes are written with an x in between two digits.

Excludes written as x's
exclude_defn.png (767 Bytes) Viewed 1190 times

Excludes are automatic when only two empty spaces remain in a nine-box.
They can also happen if only two digits remain on a row or column and they appear in the same box.
Unfortunately, excludes cannot be used to span between boxes.

When two Doubles overlap on the same two spaces, they are "upgraded" to an Exclude.
Why? The logic: If there are two slots and two digits, both digits must appear in those slots.
Doubles upgraded to an Exclude condition.
upgrade_exc.jpg (17.81 KiB) Viewed 1190 times
dokusan

Posts: 6
Joined: 03 January 2013

### Re: Non-standard pencil marks

When Doubles begin stacking up on each other, we can use the principle of pigeon-holing to discover things which would be near-impossible to realize with orthodox pencil marks.
In the following problem we have a completely empty nine-box at the upper left, along with scant information along the edges. Despite this, we are going to find the locations of 2 and 3 in this box right from the beginning.

The way to read the puzzle on the left goes as follows:
1 must go in A9, or it must go in C9.
2 must go in A7, or it must go in A9.
3 must go in C7, or it must go in C9.
7 must go in A9, or it must go in C9.

advanced.jpg (79.4 KiB) Viewed 1187 times

The m127 and m137 conditions will not suffice. If we have two empty slots and three digits, one of those digits must go. In this case, the 2's and 3's must be excluded. Because doubles remain for 2 and 3, we know without a shadow of doubt, that 2 and 3 must appear at the lower spaces. As above, the 1 and 7 are "upgraded" to an exclude condition. The 2 and 3 were pushed out, hence the name "pushing".
dokusan

Posts: 6
Joined: 03 January 2013

### Re: Non-standard pencil marks

There are some significant advantages to using standard names for well known solving techniques (and other things like cell names).

Your "pushing" puzzle solves very simply with singles alone, and does not require any of the deductions you go through.

Your logic also doesn't quite follow in the "pushing" example without at least one additional step. I don't see any way you can conclude that 7 must be in R1C1 or R1C3 without first noticing either the hidden single 7 at R2C8 or the locked candidate for 7 in R1. I suppose that another way of saying that is that you were quite terse, and it isn't obvious which approach you based your conclusion about where 7 can appear on.

Once you notice that, you have a naked pair of 17 in R1C13, which forces 2 into R3C1 and 3 into R1C3. Aside from the missing step, your approach is very standard, it just uses technique names, cell labeling, and pencil mark notation, that no one is familiar with.

Having standard terminology allows us to converse more openly, without being required to learn a new set of names for everything every time we read a post by a different poster.

JasonLion
2017 Supporter

Posts: 641
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Non-standard pencil marks

Your "doubles" sounds like nothing more or less than what is usually called "locked candidates", and your "excludes" are what the rest of us call "naked pairs". I don't see any advantages to your system over standard pencil marks--just a different (non-standard) set of terminology for the same (rather basic) techniques.

enxio27

Posts: 484
Joined: 13 November 2007

### Re: Non-standard pencil marks

dokusan wrote:Excludes are automatic when only two empty spaces remain in a nine-box.
They can also happen if only two digits remain on a row or column and they appear in the same box.
Unfortunately, excludes cannot be used to span between boxes.

Sure it can. A pair does not need to have both cells in the same box. It works just as well with two cells in the same row/column that are not in the same box.
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

### Re: Non-standard pencil marks

dokusan wrote:Six is doubled here. Doubling means that 6 must appear in one of those spaces, and nowhere else.
m6_doubled.png

If we later find that an 8 must go on top of an existing m6, then the remaining m6 is made into a real 6 automatically, without having to check it against the puzzle.
auto6.png

I use this method all the time now. John Welch's Systematic Sudoky site: http://sysudoku.com/ calls them slinks. I also found this guy who calls it "twin tagging" http://alcor.concordia.ca/~stk/sudoku/suTwinTagg.html He makes his marks differently than John Welch and I kind of like it.

Shalom
GrandPaBig
RichardGoodrich

Posts: 40
Joined: 12 December 2012
Location: Cash, Texas USA