The New Sudoku Players' Forum

[intermilan]

I'm having trouble in solving the problem as the attached image show.

I only use "basic" rules to get there:
1. if ONE unit in a row / column / square has ONE fixed value, other unites in the same row / column / square can not have this value;
2. if ONE unit in a row / column / square has a possbile value and no other units in the same row / column / square has this possbile value, this value is fixed for this row;
3. if two units in a row / column / square have the same two possible values, other units in the same row / column / square can not have these two values;
4. if two units in a row / column has a same possible value and no other units in the same row / column has this value and these two units are contained in one square, other units of the square can not have this value.
Similarly, if two units in a square has a same possible value and no other units in the same square has this value and these two units are contained in one row / column, other units of the row / column can not have this value.

I know there are more advanced techniques to apply. My intention is to implement real hardware solver and the above four rules are more feasible than those advanced rules.

Interestedly, applying the above 4 rules iteratively is able to solve quite some "hard problems". However, there are some problems I can not solve.

For the attached puzzle, anybody can give me some suggestion that what other techniques I must apply to solve the problem?

[StrmCkr]

there is a naked triple

(159) @
r4c689 => r4c1<>5

then its all singles.

[intermilan]

Thanks ...
So rules for triple chains must be used to solve hard problems ...

there is a naked triple

(159) @
r4c689 => r4c1<>5

then its all singles.

[StrmCkr]

yes and not limited to just

naked subsets.

hard problems

depends on what your considering hard.

many puzzles require alot more then just these basic logic sets to advance it to singles.

and many problems also have muti points of applicatiosn of various techniques at the same point of inferance.

for example.

you could also view the above as a hidden pair of 37 in r4c14 => r4c1<>5, r4c4<>9

[intermilan]

Well ... I missed "hidden pair" in the simple rules.

Hidden pair just evolve 2 cells, so could be feasible to implement on hardware.

3x!

[StrmCkr]

you should also consider

hidden triples and quads.
same idea.

in either box/row / column/

hidden sets are fairly easy to get working..

but naked sets are still very important i would deffinitly not avoid including these moves types.