The New Sudoku Players' Forum

[Nick67]

Now and then I like to try to solve a puzzle
with just a pen, without marking any candidates.

I just use these 2 techniques repeatedly:

1) Look at a single row (or column or block).
Check for all the cells where a 1 could go.
If there is just 1 such cell, then enter the 1 there.
Repeat this for digits 2-9 (except of course for
the digits that already appear in the group).

2) Choose one blank cell. Consider all the values
that could still be entered in that cell (based
on other values already entered in that cell's
column, row, and block). If there is only 1 value
that can still legally be entered there, then
enter that value.

These techniques are just the obvious ones,
and they are not very powerful (equivalent
to checking for hidden and naked singles with
candidates).

So I wonder: are there other techniques I could use?
(Preferably without too much brainpower required .... )

[stuartn]

With time you get to be able to do even the 'diificult' ones without writing candidates - however another simple one comes to mind. Look at a slice of rows with some entries completed ( say blocks 4,5 and 6). Look at a found number in (say) row 6 and ask yourself where it can fit in the other two blocks in the slice.

stuartn

[russ]

Now and then I like to try to solve a puzzle
with just a pen, without marking any candidates.

...

So I wonder: are there other techniques I could use?
(Preferably without too much brainpower required .... )

Try looking for a block (or column or row) where two
possible candidates are eliminated from all but two of
the block's (or column's or row's) empty cells; eg. if
all but two of the empty cells of a block are in a row
and/or a column already containing 2 *and* 4, then
those two empty cells must contain 2 and 4. So this
amounts to finding a pair. It works best for blocks in
my experience.

(I generally only note candidates for those cells with
only two candidates remaining. This avoids clutter
but does help in spotting triples, etc.)

[Nick67]

Thanks for the replies! I will try out your techniques.

Just for the record, here is a newspaper puzzle for which
my techniques failed (I was only able to add 3 numbers
to the original grid). (But I guess it likely can be solved easily
if candidates are used.)

Original puzzle:

Code: Select all

..7.6...9
.2....8..
6...3.71.
.9.7..6..
8.......4
..1..5.3.
.86.4...5
..3....2.
7...9.1..


[r.e.s.]

[...](I was only able to add 3 numbers to the original grid). (But I guess it likely can be solved easily if candidates are used.)

If you're wanting to avoid pencil-marking the candidates, in that puzzle you'll just have to deal mentally with the naked pair in col.2, and similarly with one in col.6.